scholarly journals Concurrence for a two-qubits mixed state consisting of three pure states in the framework of SU(2) coherent states

2011 ◽  
Vol 11 (2) ◽  
pp. 501-518 ◽  
Author(s):  
S. Salimi ◽  
A. Mohammadzade ◽  
K. Berrada
Keyword(s):  
Mixed State ◽  
Coherent States ◽  
Pure States

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.

scholarly journals HOW "HOT" ARE MIXED QUANTUM STATES?

2007 ◽  
Vol 05 (01n02) ◽  
pp. 311-317
Author(s):  
GEORGE PARFIONOV ◽  
ROMÀN R. ZAPATRIN
Keyword(s):  
Mixed State ◽  
Density Operator ◽  
Gibbs Distribution ◽  
The State ◽  
Quantum States ◽  
Gibbs Ensemble ◽  
Differential Entropy ◽  
Average Value ◽  
Temperature Parameter ◽  
Pure States

Given a mixed quantum state ρ of a qudit, we consider any observable M as a kind of "thermometer" in the following sense. Given a source which emits pure states with certain distributions, we select distributions such that the appropriate average value of the observable M is equal to the average Tr M ρ of M in the state ρ. Among those distributions we find the most typical, namely, having the highest differential entropy. We call this distribution the conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter β. The expressions establishing the liaisons between the density operator ρ and its temperature parameter β are provided. Within this approach, the uniform mixed state has the highest "temperature," which tends to zero as the state in question approaches a pure state.

scholarly journals Towards a Universal Measure of Complexity

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 866
Author(s):  
Jarosław Klamut ◽  
Ryszard Kutner ◽  
Zbigniew R. Struzik
Keyword(s):  
Linear Transformation ◽  
Mixed State ◽  
Degrees Of Freedom ◽  
Time Dependent ◽  
Direct Measure ◽  
System State ◽  
Dynamic Complexity ◽  
System Complexity ◽  
Pure States ◽  
Universal Measure

Recently, it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity that is based on Gell-Mann’s view of complexity. Our universal measure of complexity is based on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is the optimally mixed state consisting of pure states, i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), suitability to the analysis of system critical behaviour, and suitability to study the dynamic complexity.

scholarly journals LOCAL UNITARY EQUIVALENT CLASSES OF SYMMETRIC N-QUBIT MIXED STATES

2013 ◽  
Vol 11 (08) ◽  
pp. 1350072 ◽  
Author(s):  
SAKINEH ASHOURISHEIKHI ◽  
SWARNAMALA SIRSI
Keyword(s):  
Mixed State ◽  
Classification Scheme ◽  
Ghz State ◽  
Mixed States ◽  
Separable States ◽  
State Classification ◽  
Pure States ◽  
Two Parameters ◽  
Special Case

Majorana representation (MR) of symmetric N-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the difficulties faced in the construction of a Majorana like geometric representation for symmetric mixed state. We have overcome this problem by developing a method of classifying local unitary (LU) equivalent classes of symmetric N-qubit mixed states based on the geometrical multiaxial representation (MAR) of the density matrix. In addition to the two parameters defined for the entanglement classification of the symmetric pure states based on MR, namely, diversity degree and degeneracy configuration, we show that another parameter called rank needs to be introduced for symmetric mixed state classification. Our scheme of classification is more general as it can be applied to both pure and mixed states. To bring out the similarities/differences between the MR and MAR, N-qubit GHZ state is taken up for a detailed study. We conclude that pure state classification based on MR is not a special case of our classification scheme based on MAR. We also give a recipe to identify the most general symmetric N-qubit pure separable states. The power of our method is demonstrated using several well-known examples of symmetric two-qubit pure and mixed states as well as three-qubit pure states. Classification of uniaxial, biaxial and triaxial symmetric two-qubit mixed states which can be produced in the laboratory is studied in detail.

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.

scholarly journals The von Neumann Entropy for Mixed States

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 49 ◽  
Author(s):  
Jorge Anaya-Contreras ◽  
Héctor Moya-Cessa ◽  
Arturo Zúñiga-Segundo
Keyword(s):  
Mixed State ◽  
Infinite System ◽  
Complete System ◽  
Von Neumann Entropy ◽  
Mixed States ◽  
Field Interaction ◽  
Von Neumann ◽  
Level Atom ◽  
Quantized Field ◽  
Pure States

The Araki–Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki–Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

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