Classical pure states are coherent states

1985 ◽  
Vol 111 (8-9) ◽  
pp. 409-411 ◽  
Author(s):  
Mark Hillery
Keyword(s):  
Coherent States ◽  
Pure States

scholarly journals Entanglement in massive coupled oscillators

2011 ◽  
Vol 11 (3&4) ◽  
pp. 278-299
Author(s):  
Nathan L. Harshman ◽  
William F. Flynn
Keyword(s):  
Coupled Oscillators ◽  
Coherent States ◽  
Degrees Of Freedom ◽  
Classical Model ◽  
Reduced Density Matrix ◽  
One Dimension ◽  
Atomic Position ◽  
Pure States ◽  
Non Gaussian ◽  
Reduced Density

This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive particles with two degrees of freedom and a quadratic Hamiltonian. We present two methods, one analytic and one approximate, to calculate the interatomic entanglement for Gaussian and non-Gaussian pure states as measured by the purity of the reduced density matrix. The cases of free and trapped molecules and hetero- and homonuclear molecules are treated. In general, when the trap frequency and the molecular frequency are very different, and when the atomic masses are equal, the atoms are highly-entangled for molecular coherent states and number states. Surprisingly, while the interatomic entanglement can be quite large even for molecular coherent states, the covariance of atomic position and momentum observables can be entirely explained by a classical model with appropriately chosen statistical uncertainty.

scholarly journals Spectral distance on Lorentzian Moyal plane

2020 ◽  
Vol 17 (06) ◽  
pp. 2050089
Author(s):  
Anwesha Chakraborty ◽  
Biswajit Chakraborty
Keyword(s):  
Noncommutative Geometry ◽  
Coherent States ◽  
Euclidean Case ◽  
Spectral Triples ◽  
Spectral Distance ◽  
Moyal Plane ◽  
Pure States ◽  
Math Phys ◽  
Distance Formula

We present here a completely operatorial approach, using Hilbert–Schmidt operators, to compute spectral distances between time-like separated “events”, associated with the pure states of the algebra describing the Lorentzian Moyal plane, using the axiomatic framework given by [N. Franco, The Lorentzian distance formula in noncommutative geometry, J. Phys. Conf. Ser. 968(1) (2018) 012005; N. Franco, Temporal Lorentzian spectral triples, Rev. Math. Phys. 26(8) (2014) 1430007]. The result shows no deformations of non-commutative origin, as in the Euclidean case, if the pure states are constructed out of Glauber–Sudarshan coherent states.

A COMPARATIVE STUDY OF NEGATIVITY AND CONCURRENCE BASED ON SPIN COHERENT STATES

2010 ◽  
Vol 21 (03) ◽  
pp. 291-305 ◽  
Author(s):  
K. BERRADA ◽  
M. El BAZ ◽  
H. ELEUCH ◽  
Y. HASSOUNI
Keyword(s):  
Comparative Study ◽  
Coherent States ◽  
Mixed States ◽  
Qubit System ◽  
Entanglement Measures ◽  
Pure States ◽  
Spin Coherent States

In this paper, we investigate two different entanglement measures, the negativity and concurrence, in the case of pure and mixed states of two-qubit system basing on the spin coherent states. For two-qubit pure states, the negativity is the same as the concurrence. For mixed states, using a simplified expression of concurrence in Wootters' measure of entanglement, we write the bounds of Verstraete et al.1as a function of some new parameters and we compare the both measures for a class of mixed states.

ENTANGLEMENT MEASURE OF BIPARTITE SYSTEM STATES

2010 ◽  
Vol 07 (06) ◽  
pp. 1051-1064 ◽  
Author(s):  
K. BERRADA ◽  
Y. HASSOUNI
Keyword(s):  
Coherent States ◽  
Linear Entropy ◽  
Entanglement Measure ◽  
Mixed States ◽  
Maximal Entanglement ◽  
Bipartite System ◽  
Pure States ◽  
System States ◽  
Entangled Coherent States

Linear entropy as a measure of entanglement is applied to explain conditions for minimal and maximal entanglement of bipartite nonorthogonal pure states. We formulate this measure in terms of the amplitudes of coherent states in the case of entangled coherent states and calculate the conditions. We generalize this formalism to the case of bipartite mixed states and show that the entanglement measure is also a function of the probabilities.

Coherence measures and optimal conversion for coherent states

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1307-1316 ◽  
Author(s):  
Shuanping Du ◽  
Zhaofang Bai ◽  
Xiaofei Qi
Keyword(s):  
Relative Entropy ◽  
Pure State ◽  
Coherent States ◽  
Single Copy ◽  
Entropy Measure ◽  
General Strategy ◽  
Important Class ◽  
L1 Norm ◽  
Pure States

We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the l1-norm measure for pure states and the α-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

ENTANGLEMENT OF TWO-QUBIT NONORTHOGONAL STATES

2009 ◽  
Vol 23 (08) ◽  
pp. 2021-2027 ◽  
Author(s):  
K. BERRADA ◽  
A. CHAFIK ◽  
H. ELEUCH ◽  
Y. HASSOUNI
Keyword(s):  
Coherent States ◽  
Pure States ◽  
Spin Coherent States

We studied the entangled two-qubit nonorthogonal pure states through spin coherent states. Using the concurrence as a measure of entanglement we express it as a function of the amplitudes of those states and find conditions for maximal and minimal entanglement.

scholarly journals Entanglement of General Two-Qubit States in a Realistic Framework

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 386
Author(s):  
Sayed Abdel-Khalek ◽  
Kamal Berrada ◽  
Eied M. Khalil ◽  
Fadhel Almalki
Keyword(s):  
Quantum Entanglement ◽  
Coherent States ◽  
Mixed States ◽  
Maximal Amount ◽  
Qubit System ◽  
Pure States ◽  
Qubit States ◽  
Spin Coherent States

In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs.

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