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.

Maximally coherent states

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1355-1364
Author(s):  
Zhaofang Bai ◽  
Shuanping Du
Keyword(s):  
Quantum Information ◽  
Coherent State ◽  
Relative Entropy ◽  
Quantum Correlation ◽  
Coherent States ◽  
Entropy Measure ◽  
Product State ◽  
Quantum Operations ◽  
Maximal Entanglement

The relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we firstly investigate structural characterization of maximally coherent states with respect to the relative entropy measure. It is shown that mixed maximally coherent states do not exist and every pure maximally coherent state has the form U|ψihψ|U† , |ψi = √1 d Pd k=1 |ki, U is diagonal unitary. Based on the characterization of pure maximally coherent states, for a bipartite maximally coherent state with dA = dB, we obtain that the super-additivity equality of relative entropy measure holds if and only if the state is a product state of its reduced states. From the viewpoint of resource in quantum information, we find there exists a maximally coherent state with maximal entanglement. Originated from the behaviour of quantum correlation under the influence of quantum operations, we further classify the incoherent operations which send maximally coherent states to themselves.

scholarly journals Relations between bipartite entanglement measures

2018 ◽  
Vol 18 (1&2) ◽  
pp. 85-113 ◽  
Author(s):  
Katharina Schwaiger ◽  
Barbara Kraus
Keyword(s):  
Pure State ◽  
Single Copy ◽  
Point Of View ◽  
Multipartite Entanglement ◽  
Bipartite Entanglement ◽  
Classical Communication ◽  
Main Emphasis ◽  
Entanglement Measures ◽  
Pure States

We investigate the entanglement of bipartite systems from an operational point of view. Main emphasis is put on bipartite pure states in the single copy regime. First, we present an operational characterization of bipartite pure state entanglement, viewing the state as a multipartite state. Then, we investigate the properties and relations of two classes of operational bipartite and multipartite entanglement measures, the so-called source and the accessible entanglement. The former measures how easy it is to generate a given state via local operations and classical communication (LOCC) from some other state, whereas the latter measures the potentiality of a state to be convertible to other states via LOCC. We investigate which parameter regime is physically available, i.e. for which values of these measures does there exist a bipartite pure state. Moreover, we determine, given some state, which parameter regime can be accessed by it and from which parameter regime it can be accessed. We show that this regime can be determined analytically using the Positivstellensatz. We compute the boundaries of these sets and the boundaries of the corresponding source and accessible sets. Furthermore, we relate these results to other entanglement measures and compare their behaviors.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

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 Symmetry-like Relation of Relative Entropy Measure of Quantum Coherence

2020 ◽  
Author(s):  
Cheng-yang Zhang ◽  
Zhi-hua Guo ◽  
H.X. Cao
Keyword(s):  
Relative Entropy ◽  
Quantum Coherence ◽  
Quantum Physics ◽  
Information Science ◽  
Upper Bounds ◽  
Von Neumann Entropy ◽  
Entropy Measure ◽  
Lower And Upper Bounds ◽  
Von Neumann ◽  
Natural Logarithm

Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. In this paper, we obtain a symmetry-like relation of relative entropy measure $C_r(\rho)$ of coherence for $n$-partite quantum states $\rho$, which gives lower and upper bounds for $C_r(\rho)$. Meanwhile, we discuss the conjecture about the validity of the inequality $C_r(\rho)\leq C_{\ell_1}(\rho)$ for any state $\rho$. We observe that every mixture $\eta$ of a state $\rho$ satisfying $C_r(\rho)\leq C_{\ell_1}(\rho)$ and any incoherent state $\sigma$ also satisfies the conjecture. We also note that if the von Neumann entropy is defined by the natural logarithm $\ln$ instead of $\log_2$, then the reduced relative entropy measure of coherence $\bar{C}_r(\rho)=-\rho_{\rm{diag}}\ln \rho_{\rm{diag}}+\rho\ln \rho$ satisfies the inequality ${\bar{C}}_r(\rho)\leq C_{\ell_1}(\rho)$ for any mixed state $\rho$.

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 Pure States of Maximum Uncertainty with Respect to a Given POVM

2020 ◽  
Vol 27 (01) ◽  
pp. 2050002
Author(s):  
Anna Szymusiak
Keyword(s):  
Shannon Entropy ◽  
Pure State ◽  
Quantum States ◽  
Maximal Amount ◽  
Dimension 2 ◽  
Pure States

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter one. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how ‘badly’ can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

scholarly journals THE CHSH-TYPE INEQUALITIES FOR INFINITE-DIMENSIONAL QUANTUM SYSTEMS

2013 ◽  
Vol 27 (21) ◽  
pp. 1350151
Author(s):  
YU GUO
Keyword(s):  
Pure State ◽  
Bell Inequalities ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Pure States ◽  
Sufficient And Necessary Condition

By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a 2⊗2 subspace. We find that, for infinite-dimensional systems, the corresponding properties are similar to that of the two-qubit case: (i) The CHSH-type inequalities provide a sufficient and necessary condition for separability of pure states; (ii) The CHSH operators satisfy the Cirel'son inequalities; (iii) Any state which violates one of these Bell inequalities is distillable.

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