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Derivation of the Lindblad Generator Structure by use of the It\^o
Stochastic Calculus | We use the It\^o stochastic calculus to give a simple derivation of the
Lindblad form for the generator of a completely positive density matrix
evolution, by specialization from the corresponding global form for a
completely positive map. As a by-product, we obtain a generalized generator for
a completely positive stochastic density matrix evolution.
|
Legitimacy of wave-function expansion | In this letter we investigate the common procedure in which any wave function
is expanded into a series of eigenfunctions. It is shown that as far as
dynamical systems are concerned the expanding procedure involves various
mathematical and physical difficulties. With or without introducing phase
factors, such expansions do not represent dynamical wave functions.
|
The Encoding of Quantum State Information Within Subparticles | A method is given by which the descriptive content of quantum state
information can be encoded into subparticle coordinates. This method is
consistent with the MA-model solution to the general grand unification problem.
Subparticle mechanisms via affine or linear transformations are also discussed.
|
What is Quantum Computation? | Quantum computation is a rapidly progressing field today. What are its
principles? In what sense is it distinct from conventional computation? What
are its advantages and disadvantages? What type of problems can it address? How
practical is it to make a quantum computer? I summarise some of the important
concepts of quantum computation, in an attempt to answer these questions. A
deeper understanding of them would pave the way for future development.
|
Radiation Pressure Approach to the Repulsive Casimir Force | We study the Casimir force between a perfectly conducting and an infinitely
permeable plate with the radiation pressure approach. This method illustrates
how a repulsive force arises as a consequence of the redistribution of the
vacuum-field modes corresponding to specific boundary conditions. We discuss
also how the method of the zero-point radiation pressure follows from QED.
|
Topics in Modern Quantum Optics | This is the written version of lectures presented at "The 17th Symposium on
Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the
Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea.
|
Quantum systems coupled to a structured reservoir with multiple
excitations | We present a method for dealing with quantum systems coupled to a structured
reservoir with any density of modes and with more than one excitation. We apply
the method to a two-level atom coupled to the edge of a photonic band gap and a
defect mode. Results pertaining to this system, provide the solution to the
problem of two photons in the reservoir and possible generalization is
discussed.
|
Quantum Computers and Unstructured Search: Finding and Counting Items
with an Arbitrarily Entangled Initial State | Grover's quantum algorithm for an unstructured search problem and the Count
algorithm by Brassard et al. are generalized to the case when the initial state
is arbitrarily and maximally entangled. This ansatz might be relevant with
quantum subroutines, when the computational qubits and the environment are
coupled, and in general when the control over the quantum system is partial.
|
Comment on Identical Motion in Classical and Quantum Mechanics | Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain
classes of potentials which lead to identical classical and quantum
Hamilton-Jacobi equations. We obtain the most general form of these potential.
|
Qutrit Entanglement | We consider the separability of various joint states for N qutrits. We derive
two results: (i) the separability condition for a two-qutrit state that is a
mixture of the maximally mixed state and a maximally entangled state (such a
state is a generalization of the Werner state for two qubits); (ii) upper and
lower bounds on the size of the neighborhood of separable states surrounding
the maximally mixed state for N qutrits.
|
Continuity of Relative Entropy of Entanglement | We show that an entanglement measure called relative entropy of entanglement
satisfies a strong continuity condition. If two states are close to each other
then so are their entanglements per particle pair in this measure. It follows
in particular, that the measure is appropriate for the description of
entanglement manipulations in the limit of an infinite number of pairs of
particles.
|
Exact solutions of nonstationary Schredinger equations and geometric
phase | A procedure of solving nonstationary Schredinger equations in the exact
analytic form is elaborated on the basis of exactly solvable stationary models.
The exact solutions are employed to study the nonadiabatic geometric phase.
|
NMR quantum computation with indirectly coupled gates | An NMR realization of a two-qubit quantum gate which processes quantum
information indirectly via couplings to a spectator qubit is presented in the
context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive
NMR implementation of the Deutsch-Jozsa algorithm for functions with three
argument bits and demonstrates a technique essential for multi-qubit quantum
computation.
|
Evolution loops and spin-1/2 systems | The derivation of a new family of magnetic fields inducing exactly solvable
spin evolutions is presented. The conditions for which these fields generate
the evolution loops (dynamical processes for which any spin state evolves
cyclically) are studied. Their natural connection with geometric phases and the
corresponding calculation is also elaborated.
|
Backlund-type superposition and free particle n-susy partners | The higher order susy partners of Schroedinger Hamiltonians can be explicitly
constructed by iterating a nonlinear difference algorithm coinciding with the
Backlund superposition principle used in soliton theory. As an example, it is
applied in the construction of new higher order susy partners of the free
particle potential, which can be used as a handy tool in soliton theory.
|
On Symmetries in Nonlinear Quantum Mechanics | It is shown how nonlinear versions of quantum mechanics can be refolmulated
in terms of a (linear) C*-algebraic theory. Then also their symmetries are
described as automorphisms of the correspondong C*-algebra. The requirement of
"conservation of transition probabilities" is discussed.
|
Intermediate coherent-phase(PB) states of radiation fields and their
nonclassical properties | Intermediate states interpolating coherent states and Pegg-Barnett phase
states are investigated using the ladder operator approach. These states reduce
to coherent and Pegg-Barnett phase states in two different limits. Statistical
and squeezing properties are studied in detail.
|
The supersymmetric modified Poschl-Teller and delta-well potentials | New supersymmetric partners of the modified Poschl-Teller and the Dirac's
delta well potentials are constructed in closed form. The resulting
one-parametric potentials are shown to be interrelated by a limiting process.
The range of values of the parameters for which these potentials are free of
singularities is exactly determined. The construction of higher order
supersymmetric partner potentials is also investigated.
|
Distillability and partial transposition in bipartite systems | We study the distillability of a certain class of bipartite density operators
which can be obtained via depolarization starting from an arbitrary one. Our
results suggest that non-positivity of the partial transpose of a density
operator is not a sufficient condition for distillability, when the dimension
of both subsystems is higher than two.
|
Quantum State Reconstruction Using Atom Optics | We present a novel technique in which the total internal quantum state of an
atom may be reconstructed via the measurement of the momentum transferred to an
atom following its interaction with a near resonant travelling wave laser beam.
We present the first such measurement and demonstrate the feasibility of the
technique.
|
Decoherence via Dynamical Casimir Effect | We derive a master equation for a mirror interacting with the vacuum field
via radiation pressure. The dynamical Casimir effect leads to decoherence of a
'Schroedinger cat' state in a time scale that depends on the degree of
'macroscopicity' of the state components, and which may be much shorter than
the relaxation time scale. Coherent states are selected by the interaction as
pointer states.
|
Measuring quantum state overlaps of traveling optical fields | We propose a detection scheme for measuring the overlap of the quantum state
of a weakly excited traveling-field mode with a desired reference quantum
state, by successive mixing the signal mode with modes prepared in coherent
states and performing photon-number measurements in an array of beam splitters.
To illustrate the scheme, we discuss the measurement of the quantum phase and
the detection of Schrodinger-cat-like states.
|
Almost-Everywhere Superiority for Quantum Computing | Simon as extended by Brassard and H{\o}yer shows that there are tasks on
which polynomial-time quantum machines are exponentially faster than each
classical machine infinitely often. The present paper shows that there are
tasks on which polynomial-time quantum machines are exponentially faster than
each classical machine almost everywhere.
|
Relativistic quantum coin tossing | A relativistic quantum information exchange protocol is proposed allowing two
distant users to realize ``coin tossing'' procedure. The protocol is based on
the point that in relativistic quantum theory reliable distinguishing between
the two orthogonal states generally requires a finite time depending on the
structure of these states.
|
Locally curved quantum layers | We consider a quantum particle constrained to a curved layer of a constant
width built over an infinite smooth surface. We suppose that the latter is a
locally deformed plane and that the layer has the hard-wall boundary. Under
this assumptions we prove that the particle Hamiltonian possesses geometrically
induced bound states.
|
On mechanisms that enforce complementarity | In a recent publication Luis and Sanchez-Soto arrive at the conclusion that
complementarity is universally enforced by random classical phase kicks. We
disagree. One could just as well argue that quantum entanglement is the
universal mechanism. Both claims of universality are unjustified, however.
|
Refined Factorizations of Solvable Potentials | A generalization of the factorization technique is shown to be a powerful
algebraic tool to discover further properties of a class of integrable systems
in Quantum Mechanics. The method is applied in the study of radial oscillator,
Morse and Coulomb potentials to obtain a wide set of raising and lowering
operators, and to show clearly the connection that link these systems.
|
The Photon-Box Bohr-Einstein Debate Demithologized | The legendary discussion between Einstein and Bohr concerning the photon box
experiment is critically analyzed. It is shown that Einstein's argument is
flawed and Bohr's reply is wrong.
|
Measuring the entanglement of bipartite pure states | The problem of the experimental determination of the amount of entanglement
of a bipartite pure state is addressed. We show that measuring a single
observable does not suffice to determine the entanglement of a given unknown
pure state of two particles. Possible minimal local measuring strategies are
discussed and a comparison is made on the basis of their best achievable
precision.
|
Scattering of relativistic particles by a Coulomb field in two
dimensions | The scattering of relativistic Dirac particles by a Coulomb field $\pm
Ze^2/r$ in two dimensions is studied and the scattering amplitude is obtained
as a partial wave series. For small $Z$ the series can be summed up
approximately to give a closed form. The result, though being aproximate,
exhibites some nonperturbative feature and cannot be obtained from perturbative
quantum electrodynamics at the tree level.
|
Reduced phase space quantization | We examine two singular Lagrangian systems with constraints which apparently
reduce the phase space to a 2-dimensional sphere and a 2-dimensional
hyperboloid. Rigorous constraint analysis by Dirac's method, however, gives
2-dimensional open disc and an infinite plane with a hole in the centre
respectively as the reduced phase spaces. Upon canonical quantisation the
classical constraints show up as restrictions on the Hilbert space.
|
Generalized Algebraic Bargmann - Darboux Transformations | Algebraic Bargmann and Darboux transformations for equations of a more
general form than the Schr\"odinger ones with an additional functional
dependence h(r) in the right-hand side of equations are constructed. The
suggested generalized transformations turn into the Bargmann and Darboux
transformations for both fixed and variable values of energy and an angular
momentum.
|
Barrier Penetration for Supersymmetric Shape-Invariant Potentials | Exact reflection and transmission coefficients for supersymmetric
shape-invariant potentials barriers are calculated by an analytical
continuation of the asymptotic wave functions obtained via the introduction of
new generalized ladder operators. The general form of the wave function is
obtained by the use of the F-matrix formalism of Froman and Froman which is
related to the evolution of asymptotic wave function coefficients.
|
Entangled Coherent State Qubits in an Ion Trap | We show how entangled qubits can be encoded as entangled coherent states of
two-dimensional centre-of-mass vibrational motion for two ions in an ion trap.
The entangled qubit state is equivalent to the canonical Bell state, and we
introduce a proposal for entanglement transfer from the two vibrational modes
to the electronic states of the two ions in order for the Bell state to be
detected by resonance fluorescence shelving methods.
|
Quantum Reed-Solomon Codes | After a brief introduction to both quantum computation and quantum error
correction, we show how to construct quantum error-correcting codes based on
classical BCH codes. With these codes, decoding can exploit additional
information about the position of errors. This error model - the quantum
erasure channel - is discussed. Finally, parameters of quantum BCH codes are
provided.
|
Quantum BCH Codes | After a brief introduction to both quantum computation and quantum error
correction, we show how to construct quantum error-correcting codes based on
classical BCH codes. With these codes, decoding can exploit additional
information about the position of errors. This error model - the quantum
erasure channel - is discussed. Finally, parameters of quantum BCH codes are
provided.
|
Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers | We transfer the concept of linear feed-back shift registers to quantum
circuits. It is shown how to use these quantum linear shift registers for
encoding and decoding cyclic quantum error-correcting codes.
|
Comparison between quantum and classical dynamics in the effective
action formalism | No abstract available
|
Quantum chaos in quantum Turing machines | We investigate a 2-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. We demonstrate that a single chaotic parameter input \alpha_m
leads to a chaotic dynamics in the entire Hilbert-space.
|
Note on Coherent States and Adiabatic Connections, Curvatures | We give a possible generalization to the example in the paper of Zanardi and
Rasetti (quant-ph/9904011). For this generalized one explicit forms of
adiabatic connection, curvature and etc. are given.
|
WKB and MAF Quantization Rules for Spatially Confined Quantum Mechanical
Systems | A formalism is developed to obtain the energy eigenvalues of spatially
confined quantum mechanical systems in the framework of The usual WKB and MAF
methods. The technique is applied to three different cases,viz one dimensional
Harmonic Oscillators,Quartic Oscillators and a boxed-in charged particle in
electric field.
|
Popper's experiment and the Copenhagen interpretation | Popper conceived an experiment whose analysis led to a result that he deemed
absurd. Popper wrote that his reasoning was based on the Copenhagen
interpretation and therefore invalidated the latter. Actually, Popper's
argument involves counterfactual reasoning and violates Bohr's complementarity
principle. The absurdity of Popper's result only confirms Bohr's approach.
|
Purification of impure density operators and the recovery of
entanglements | The need to retain the relative phases in quantum mechanics implies an
addition law parametrized by a phase of two density operators required for the
purification of a density matrix. This is shown with quantum tomography and the
Wigner function. Entanglement is determined in terms of phase dependent
multiplication.
|
The Holevo bound and Landauer's principle | Landauer's principle states that the erasure of information generates a
corresponding amount of entropy in the environment. We show that Landauer's
principle provides an intuitive basis for Holevo bound on the classical
capacity of a quantum channel.
|
Quantum CPU and Quantum Simulating | Making use of an universal quantum network or QCPU proposed by me [6], some
special quantum networks for simulating some quantum systems are given out.
Specially, it is obtained that the quantum network for the time evolution
operator which can simulate, in general, Schr\"odinger equation.
|
Quantum CPU and Quantum Algorithm | Making use of an universal quantum network -- QCPU proposed by
me\upcite{My1}, it is obtained that the whole quantum network which can
implement some the known quantum algorithms including Deutsch algorithm,
quantum Fourier transformation, Shor's algorithm and Grover's algorithm.
|
Testing operational phase concepts in quantum optics | An experimental comparison of several operational phase concepts is
presented. In particular, it is shown that statistically motivated evaluation
of experimental data may lead to a significant improvement in phase fitting
upon the conventional Noh, Fouge'res and Mandel procedure. The analysis is
extended to the asymptotic limit of large intensities, where a strong evidence
in favor of multi--dimensional estimation procedures has been found.
|
Nonlinear Optics and Quantum Entanglement of Ultra-Slow Single Photons | Two light pulses propagating with ultra-slow group velocities in a coherently
prepared atomic gas exhibit dissipation-free nonlinear coupling of an
unprecedented strength. This enables a single-photon pulse to coherently
control or manipulate the quantum state of the other. Processes of this kind
result in generation of entangled states of radiation field and open up new
prospectives for quantum information processing.
|
Quantum Mechanics as a Principle Theory | I show how quantum mechanics, like the theory of relativity, can be
understood as a 'principle theory' in Einstein's sense, and I use this notion
to explore the approach to the problem of interpretation developed in my book
Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).
|
Revised Proof of the Uniqueness Theorem for 'No Collapse'
Interpretations of Quantum Mechanics | We show that the Bub-Clifton uniqueness theorem for 'no collapse'
interpretations of quantum mechanics (Studies in the History and Philosophy of
Modern Physics 27, 181-219 (1996)) can be proved without the 'weak
separability' assumption.
|
Quantum gates using two-electron states of triple quantum dot | Quantum computation using electron spins in three coupled dot with different
size is proposed. By using the energy selectivity of both photon assisted
tunneling and spin rotation of electrons, logic gates are realized by static
and rotational magnetic field and resonant optical pulses. Possibility of
increasing the number of quantum bits using the energy selectivity is also
discussed.
|
Quantum revivals, geometric phases and circle map recurrences | Revivals of the coherent states of a deformed, adiabatically and cyclically
varying oscillator Hamiltonian are examined. The revival time distribution is
exactly that of Poincar\'{e} recurrences for a rotation map: only three
distinct revival times can occur, with specified weights. A link is thus
established between quantum revivals and recurrences in a coarse-grained
discrete-time dynamical system.
|
On Rotating a Qubit | The state function of a quantum object is undetermined with respect to its
phase. This indeterminacy does not matter if it is global, but what if the
components of the state have unknown relative phases? Can useful computations
be performed in spite of this local indeterminacy? We consider this question in
relation to the problem of the rotation of a qubit and examine its broader
implications for quantum computing.
|
Quantum probability from a geometrical interpretation of a wave function | The probabilistic prediction of quantum theory is mystery. I solved the
mystery by a geometrical interpretation of a wave function. This suggests the
unification between quantum theory and the theory of relativity. This suggests
Many-Worlds Interpretation is true, too.
|
Van Hove's "\lambda^2 t" limit in nonrelativistic and relativistic
field-theoretical models | Van Hove's "\lambda^2 t" limiting procedure is analyzed in some interesting
quantum field theoretical cases, both in nonrelativistic and relativistic
models. We look at the deviations from a purely exponential behavior in a decay
process and discuss the subtle issues of state preparation and initial time.
|
A Comment on Fisher Information and Quantum Algorithms | We show that Grover's algorithm defines a geodesic in quantum Hilbert space
with the Fubini-Study metric. From statistical point of view Grover's algorithm
is characterized by constant Fisher's function. Quantum algorithms changing
complexity class as Shor's factorization does not preserve constant Fisher's
information. An adiabatic quantum factorization algorithm in non polynomial
time is presented to exemplify the result.
|
Quantum Instantons and Quantum Chaos | Based on a closed form expression for the path integral of quantum transition
amplitudes, we suggest rigorous definitions of both, quantum instantons and
quantum chaos. As an example we compute the quantum instanton of the double
well potential.
|
Dynamical mass shift for a partially reflecting moving mirror | We consider the vacuum fluctuations contribution to the mass of a mirror in
an exactly soluble partially reflecting moving mirror model. Partial
reflectivity is accounted for by a repulsive delta-type potential localized
along the mirror trajectory. The mirror's mass is explicitly found as an
integral functional of the mirror's past trajectory.
|
Exactly Solvable Model of Quantum Spin Interacting with Spin Environment | An exactly solvable model of a quantum spin interacting with a spin
environment is considered. The interaction is chosen to be such that the state
of the environment is conserved. The reduced density matrix of the spin is
calculated for arbitrary coupling strength and arbitrary time. The stationary
state of the spin is obtained explicitely in the $t \to \infty$ limit.
|
Opposite momenta lead to opposite directions | When a particle decays into two fragments, the wavefunctions of the latter
are spherical shells with expanding radii. In spite of this spherical symmetry,
the two particles can be detected only in opposite directions.
|
Filtering Number States of the Vibrational Motion of an Ion | We propose a scheme to generate number states (and specific superpositions of
them) of the vibrational motion of a trapped ion. In particular, we show that
robust to noise qubits can be generated with arbitrary amplitudes.
|
Optimal estimation of two-qubit pure-state entanglement | We present optimal measuring strategies for the estimation of the
entanglement of unknown two-qubit pure states and of the degree of mixing of
unknown single-qubit mixed states, of which N identical copies are available.
The most general measuring strategies are considered in both situations, to
conclude in the first case that a local, although collective, measurement
suffices to estimate entanglement, a non-local property, optimally.
|
Constructing quantum error-correcting codes for p^m-state systems from
classical error-correcting codes | We generalize the construction of quantum error-correcting codes from
GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how
to determine the error from a syndrome. Finally we discuss a systematic
construction of quantum codes with efficient decoding algorithms.
|
NMR spectroscopy and computing beyond myth and fiction | Only craziness I am ashamed about.
|
Faster Than Light Communication | This paper has been withdrawn by the author, due a crucial error in the main
idea.
|
Semiclassical Approximation for Periodic Potentials | We derive the semiclassical WKB quantization condition for obtaining the
energy band edges of periodic potentials. The derivation is based on an
approach which is much simpler than the usual method of interpolating with
linear potentials in the regions of the classical turning points. The band
structure of several periodic potentials is computed using our semiclassical
quantization condition.
|
Faster than light Bell telephone of Michalski transmits only noise | Motivated by pedagogical reasons we pinpoint the mistake in the recent claim,
in quant-ph/9911016, that faster than light communication is possible.
|
Evolution of fermionic systems as an expectation over Poisson processes | We derive an exact probabilistic representation for the evolution of a
Hubbard model with site- and spin-dependent hopping coefficients and
site-dependent interactions in terms of an associated stochastic dynamics of a
collection of Poisson processes.
|
An application of two photon entangled states to quantum metrology | Besides many interesting application to the study of foundations of quantum
mechanics, entangled state are now assuming a large relevance for some
practical application. In particular, we discuss most recent results obtained
in our laboratory on the use of two photons entangled states produced in
parametric down conversion for absolute quantum efficiency calibration of
photodetectors, in photon counting regime.
|
An Operator Formulation of Classical Mechanics and Semiclassical Limit | The generalized h-dependent operator algebra is defined ($0\leq h \leq h_o$).
For h= h_o it becomes equivalent to the quantum mechanical algebra of
observables and for h=0 it is equivalent to the classical one. We show this by
proposing how the main features of both mechanics can be defined in operator
form.
|
Optical Bell Measurement by Fock Filtering | We describe a nonlinear interferometric setup to perform a complete optical
Bell measurement, i.e. to unambigously discriminate the four polarization
entangled EPR-Bell photon pairs. The scheme is robust against detector
inefficiency.
|
Quantum Statistical Mechanics on a Quantum Computer | We describe a quantum algorithm to compute the density of states and thermal
equilibrium properties of quantum many-body systems. We present results
obtained by running this algorithm on a software implementation of a 21-qubit
quantum computer for the case of an antiferromagnetic Heisenberg model on
triangular lattices of different size.
|
Quantum Spin Dynamics and Quantum Computation | We describe a simulation method for a quantum spin model of a generic,
general purpose quantum computer. The use of this quantum computer simulator is
illustrated through several implementations of Grover's database search
algorithm. Some preliminary results on the stability of quantum algorithms are
presented.
|
Greenberger-Horne-Zeilinger paradoxes with symmetric multiport beam
splitters | In a gedankenexperiment N particles in a generalized GHZ-type beam entangled
state (each particle can be in one of M beams) are fed into N symmetric 2M-port
beam splitters (spatially separated). Correlation functions for such a process
(using the Bell numbers value assignment approach) reveal a remarkable
symmetry. For N=M+1 greater or equal to 4 a series of GHZ paradoxes are shown.
|
Quantum Computer Emulator | We describe a quantum computer emulator for a generic, general purpose
quantum computer. This emulator consists of a simulator of the physical
realization of the quantum computer and a graphical user interface to program
and control the simulator. We illustrate the use of the quantum computer
emulator through various implementations of the Deutsch-Jozsa and Grover's
database search algorithm.
|
Cheat Sensitive Quantum Bit Commitment | We define cheat sensitive cryptographic protocols between mistrustful parties
as protocols which guarantee that, if either cheats, the other has some nonzero
probability of detecting the cheating. We give an example of an unconditionally
secure cheat sensitive non-relativistic bit commitment protocol which uses
quantum information to implement a task which is classically impossible; we
also describe a simple relativistic protocol.
|
Entanglement swapping with PDC sources | We show that the possibility of distinguishing between single and two photon
detection events is not a necessary requirement for the proof that recent
operational realization of entanglement swapping cannot find a local realistic
description. We propose a simple modification of the experiment, which gives a
richer set of interesting phenomena.
|
Motion of a spin 1/2 particle in shape invariant scalar and magnetic
fields | We study the motion of a spin 1/2 particle in a scalar as well as a magnetic
field within the framework of supersymmetric quantum mechanics(SUSYQM). We also
introduce the concept of shape invariant scalar and magnetic fields and it is
shown that the problem admits exact analytical solutions when such fields are
considered.
|
Large Numbers, the Chinese Remainder Theorem, and the Circle of Fifths | This is a pedagogical article cited in the foregoing research note,
quant-ph/9911050
|
Coherent states, Yang-Mills theory, and reduction | This paper explains some of the ideas behind a prior joint work of the author
with Bruce Driver on the canonical quantization of Yang-Mills theory on a
spacetime cylinder. The idea is that the generalized Segal-Bargmann transform
for a compact group can be obtained from the ordinary Segal-Bargmann transform
by imposing gauge symmetry.
|
Construction of quantum states with bound entanglement | We present a new family of bound-entangled quantum states in 3x3 dimensions.
Their density matrix depends on 7 independent parameters and has 4 different
non-vanishing eigenvalues.
|
Time-dependent Perturbation Theory in Quantum Mechanics | After revealing difficulties of the standard time-dependent perturbation
theory in quantum mechanics mainly from the viewpoint of practical calculation,
we propose a new quasi-canonical perturbation theory. In the new theory, the
dynamics of physical observables, instead of that of coefficients of
wave-function expansion, is formulated so that the gauge-invariance and
correspondence principles are observed naturally.
|
Semiclassical limit of the Dirac equation and spin precession | We study the Dirac equation with slowly varying external potentials. Using
matrix-valued Wigner functions we prove that the electron follows with high
precision the classical orbit and that the spin precesses according to the BMT
equation with gyromagnetic ratio g=2.
|
Quantum theory of incompatible observations | Maximum likelihood principle is shown to be the best measure for relating the
experimental data with the predictions of quantum theory.
|
Reconstruction of the spin state | System of 1/2 spin particles is observed repeatedly using Stern-Gerlach
apparatuses with rotated orientations. Synthesis of such non-commuting
observables is analyzed using maximum likelihood estimation as an example of
quantum state reconstruction. Repeated incompatible observations represent a
new generalized measurement. This idealized scheme will serve for analysis of
future experiments in neutron and quantum optics.
|
Motional Squashed States | We show that by using a feedback loop it is possible to reduce the
fluctuations in one quadrature of the vibrational degree of freedom of a
trapped ion below the quantum limit. The stationary state is not a proper
squeezed state, but rather a ``squashed'' state, since the uncertainty in the
orthogonal quadrature, which is larger than the standard quantum limit, is
unaffected by the feedback action.
|
Semiclassical wave equation and exactness of the WKB method | The exactness of the semiclassical method for three-dimensional problems in
quantum mechanics is analyzed. The wave equation appropriate in the
quasiclassical region is derived. It is shown that application of the standard
leading-order WKB quantization condition to this equation reproduces exact
energy eigenvalues for all solvable spherically symmetric potentials.
|
Relativistic semiclassical wave equation and its solution | The properties of relativistic particles in the quasiclassical region are
investigated. The relativistic semiclassical wave equation appropriate in the
quasiclassical region is derived. It is shown that the leading-order WKB
quantization rule is the appropriate method to solve the equation obtained.
|
Off-Diagonal Geometric Phases | We investigate the adiabatic evolution of a set of non-degenerate eigenstates
of a parameterized Hamiltonian. Their relative phase change can be related to
geometric measurable quantities that extend the familiar concept of Berry phase
to the evolution of more than one state. We present several physical systems
where these concepts can be applied, including an experiment on microwave
cavities for which off-diagonal phases can be determined from published data.
|
Withdrawn paper | Only craziness I am ashamed about.
|
Radiation of a quantum localized source | New effective operators, describing the photons with given polarization at
given position with respect to a source are proposed. These operators can be
used to construct the near and intermediate zones quantum optics. It is shown
that the use of the conventional plane photons can lead to a wrong results for
quantum fluctuations of polarization even in the far zone.
|
Quantum fluctuations of the angular momentum and energy of the ground
state | Quasiclassical solution of the three-dimensional Schredinger's equation is
given. The existence of nonzero minimal angular momentum M_0 = \hbar /2 is
shown, which corresponds to the quantum fluctuations of the angular momentum
and contributes to the energy of the ground state.
|
Relativistic Quantum Computing | We present some informal remarks on aspects of relativistic quantum
computing.
|
A remark on the isotropic model | The applicability of the so-called isotropic and anisotropic complete
photonic-band-gap (CPBG) models [S. John and J. Wang, Phys. Rev. Lett. {\bf
64}, 2418 (1990)] to capture essential features of the spontaneous emission
(SE) of a fluorescent atom or molecule near a band-gap-edge of a CPBG structure
is discussed.
|
A model independent approach to non dissipative decoherence | We consider the case when decoherence is due to the fluctuations of some
classical variable or parameter of a system and not to its entanglement with
the environment. Under few and quite general assumptions, we derive a
model-independent formalism for this non-dissipative decoherence, and we apply
it to explain the decoherence observed in some recent experiments in cavity QED
and on trapped ions.
|
Improving Detectors Using Entangling Quantum Copiers | We present a detection scheme which using imperfect detectors, and imperfect
quantum copying machines (which entangle the copies), allows one to extract
more information from an incoming signal, than with the imperfect detectors
alone.
|
A new PT symmetric complex Hamiltonian with a real spectra | We construct an isospectrum systems in terms of a real and complex potential
to show that the underlying PT symmetric Hamiltonian possesses a real spectrum
which is shared by its real partner.
|
Temperature Variation of Ultra Slow Light in a Cold Gas | A model is developed to explain the temperature dependence of the group
velocity as observed in the experiments of Hau et al (Nature {\bf397}, 594
(1999)). The group velocity is quite sensitive to the change in the spatial
density. The inhomogeneity in the density and its temperature dependence are
primarily responsible for the observed behavior.
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Time scales in quantum mechanics by a scattering map | Inside quantum mechanics the problem of decoherence for an isolated, finite
system is linked to a coarse-grained description of its dynamics.
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Shape invariant potentials with PT symmetry | Suitable complexification of the well known solvable oscillators in one
dimension is shown to give the four exactly solvable models which combine the
shape- and PT-invariance.
In version v2 the result is extended of the s-wave shape-invariant forces.
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