Construction of quantum states from an optimally truncated von Neumann lattice of coherent states

1999 ◽  
Vol 32 (17) ◽  
pp. 3169-3178 ◽  
Author(s):  
L K Stergioulas ◽  
V S Vassiliadis ◽  
A Vourdas
Keyword(s):  
Coherent States ◽  
Quantum States ◽  
Von Neumann

A COMPARISON BETWEEN WEHRL–LIEB AND VON NEUMANN ENTROPIES FOR TIME-EVOLVING SPIN-1/2 MIXED STATES

1994 ◽  
Vol 08 (16) ◽  
pp. 995-1006 ◽  
Author(s):  
S. S. MIZRAHI ◽  
V. V. DODONOV ◽  
D. OTERO
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Alternative Formulation ◽  
Spin States ◽  
Continuous Representation ◽  
Commun Math Phys ◽  
Mixed States ◽  
Von Neumann ◽  
Math Phys

Years ago, A. Wehrl (Rev. Mod. Phys.50, 221 (1978)) introduced the concept of classicallike entropy of quantum states when a two-label continuous representation is used; for instance, the harmonic oscillator coherent states. Subsequently, E. H. Lieb (Commun. Math. Phys.62, 35 (1978)) extended that concept of entropy to the Bloch coherent spin states. Here, we consider spin-1/2 systems and calculate both the Wehrl–Lieb and von Neumann entropies, and then we compare the results and discuss the Wehrl–Lieb entropy as an alternative formulation to von Neumann's. As illustration, three examples are worked out: (i) the decoherence of a quantum state in a measurement process, (ii) the conservation of coherence, and (iii) the recoherence phenomena that appear in the solutions of a specific master equation that originates from a nonlinear Schrödinger equation.

scholarly journals Zero uncertainty states in the presence of quantum memory

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Huangjun Zhu
Keyword(s):  
Uncertainty Principle ◽  
Quantum States ◽  
Quantum Memory ◽  
System State ◽  
Von Neumann ◽  
Practical Applications ◽  
Classical Information ◽  
Fundamental Limit ◽  
Minimum Uncertainty ◽  
Incompatible Observables

AbstractThe uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Zero uncertainty states (in contrast with minimum uncertainty states) are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all zero uncertainty states of any given set of nondegenerate observables and determine the minimum entanglement required. It turns out all zero uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a simple and precise connection between zero uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

scholarly journals Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

2010 ◽  
Vol 82 (6) ◽  
Author(s):  
Marco Barbieri ◽  
Nicolò Spagnolo ◽  
Marco G. Genoni ◽  
Franck Ferreyrol ◽  
Rémi Blandino ◽  
...  
Keyword(s):  
Experimental Test ◽  
Coherent States ◽  
Single Photon ◽  
Quantum States

Homodyne-like detection scheme based on photon-number-resolving detectors

2017 ◽  
Vol 15 (08) ◽  
pp. 1740016 ◽  
Author(s):  
Alessia Allevi ◽  
Matteo Bina ◽  
Stefano Olivares ◽  
Maria Bondani
Keyword(s):  
Coherent States ◽  
Beam Splitter ◽  
Photon Number ◽  
Local Oscillator ◽  
Quantum States ◽  
Homodyne Detection ◽  
Detection Scheme ◽  
Light Signals ◽  
The Difference ◽  
Signal Field

Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.

PARASUPERSYMMETRIC COHERENT STATES FOR LANDAU LEVELS WITH DYNAMICAL SYMMETRY GROUP H4

2002 ◽  
Vol 17 (28) ◽  
pp. 4081-4093 ◽  
Author(s):  
H. FAKHRI ◽  
H. MOTAVALI
Keyword(s):  
Magnetic Field ◽  
Symmetry Group ◽  
Coherent States ◽  
Ad Hoc ◽  
Flat Surface ◽  
Arbitrary Order ◽  
Dynamical Symmetry ◽  
Quantum States ◽  
Landau Levels ◽  
Lowering Operator

The eigenstates and their degeneracy for parasupersymmetric Hamiltonian of arbitrary order p, corresponding to the motion of a charged particle with spin [Formula: see text] on the flat surface in the presence of a constant magnetic field along z-axis, are calculated. The eigenstates are expressed in terms of Landau levels quantum states with dynamical symmetry group H4. Furthermore, parasupersymmetric coherent states with multiplicity degeneracy are derived for an ad hoc lowering operator of the eigenstates in terms of ordinary coherent states of Landau Hamiltonian.

COLLAPSE AND REVIVAL EFFECT IN A MESOSCOPIC LC CIRCUIT

2004 ◽  
Vol 18 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
HAI-MEI LUO ◽  
YING-HUA JI ◽  
JIE LIU
Keyword(s):  
Time Evolution ◽  
Dynamic Behavior ◽  
Quantum State ◽  
Tunnel Junction ◽  
Coherent States ◽  
The State ◽  
Quantum States ◽  
Quantum Superposition ◽  
Coupling Energy ◽  
Lc Circuit

This paper studied the time evolution of quantum state in a mesoscopic LC circuit with the coupling energy caused by mesoscopic capacitor acting as a tunnel junction. It indicates that the state of the junction evolves into the quantum superposition of two coherent states and, in the state, nonclassical squeezing properties of the circuit appear. It also indicates that the dynamic behavior of the current shows collapse and revival phenomenon. The research in the paper will be helpful to miniaturize integrate circuits and electric components. It will be also important for the utilization of mesoscopic circuits to evolve the quantum states, which work as information carriers.

scholarly journals A CLASS OF QUANTUM STATES WITH CLASSICAL-LIKE EVOLUTION

1994 ◽  
Vol 08 (29) ◽  
pp. 1823-1831 ◽  
Author(s):  
SALVATORE DE MARTINO ◽  
SILVIO DE SIENA ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Time Dependent ◽  
Stationary States ◽  
Oscillator Potential ◽  
Classical Motion ◽  
Stochastic Formulation ◽  
New States

In the framework of the stochastic formulation of quantum mechanics we derive non-stationary states for a class of time-dependent potentials. The wave packets follow a classical motion with constant dispersion. The new states define a possible extension of the harmonic oscillator coherent states. As an explicit application, we study a sestic oscillator potential.

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