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 Common Coherence Witnesses and Common Coherent States

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1136
Author(s):  
Bang-Hai Wang ◽  
Zi-Heng Ding ◽  
Zhihao Ma ◽  
Shao-Ming Fei
Keyword(s):  
Coherent State ◽  
Coherent States ◽  
State Problem ◽  
Properties And Characterization ◽  
The Common ◽  
High Level

We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,⋯,Wn can detect some common coherent states if and only if ∑i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,⋯,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.

APPLICATION OF PAIR COHERENT STATES IN QUANTUM INFORMATION PROCESSES

2004 ◽  
Vol 18 (17) ◽  
pp. 913-921 ◽  
Author(s):  
RU-KUAN WU ◽  
SHANG-BIN LI ◽  
QIN-MEI WANG ◽  
JING-BO XU
Keyword(s):  
Quantum Information ◽  
Relative Entropy ◽  
Coherent States ◽  
Phase Damping ◽  
Information Processes ◽  
Relative Entropy Of Entanglement

We investigate the entanglement of pair coherent states in the phase damping channel by adopting the relative entropy of entanglement and propose a protocol of teleportation via pair coherent states. The fidelity of the protocol is then analyzed and the influence of phase damping on the teleportation fidelity examined.

scholarly journals Coherent preorder of quantum states

2020 ◽  
Vol 20 (13&14) ◽  
pp. 1124-1137
Author(s):  
Zhaofang Bai ◽  
Shuanping Shuanping Du
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Coherent States ◽  
Quantum Coherence ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Mixed States ◽  
Quantum Hypothesis ◽  
Quantum Hypothesis Testing

As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $(\rho_1,\rho_2)$ and $(\sigma_1,\sigma_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $\Phi$ such that $\Phi(\rho_i) =\sigma_i,i = 1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation from rank-two mixed coherent states to $q$-level maximally coherent states. In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

Characterization of several kinds of quantum analogues of relative entropy

2006 ◽  
Vol 6 (7) ◽  
pp. 583-596
Author(s):  
M. Hayashi
Keyword(s):  
Quantum Information ◽  
Relative Entropy ◽  
Quantum Relative Entropy

Quantum relative entropy $D(\rho\|\sigma)\defeq\Tr \rho (\log \rho- \log \sigma)$ plays an important role in quantum information and related fields. However, there are many quantum analogues of relative entropy. In this paper, we characterize these analogues from information geometrical viewpoint. We also consider the naturalness of quantum relative entropy among these analogues.

Monotonicity of quantum relative entropy and recoverability

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1333-1354 ◽  
Author(s):  
Mario Berta ◽  
Marius Lemm ◽  
Mark M. Wilde
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Relative Entropy ◽  
Remainder Term ◽  
Conditional Entropy ◽  
Quantum Information Theory ◽  
Partial Trace ◽  
Quantum Operations ◽  
Strong Subadditivity ◽  
Joint Convexity

The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term for this inequality that quantifies how well one can recover from a loss of information by employing a rotated Petz recovery map. The main approach for proving this refinement is to combine the methods of [Fawzi and Renner, 2014] with the notion of a relative typical subspace from [Bjelakovic and Siegmund-Schultze, 2003]. Our paper constitutes partial progress towards a remainder term which features just the Petz recovery map (not a rotated Petz map), a conjecture which would have many consequences in quantum information theory. A well known result states that the monotonicity of relative entropy with respect to quantum operations is equivalent to each of the following inequalities: strong subadditivity of entropy, concavity of conditional entropy, joint convexity of relative entropy, and monotonicity of relative entropy with respect to partial trace. We show that this equivalence holds true for refinements of all these inequalities in terms of the Petz recovery map. So either all of these refinements are true or all are false.

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.

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.

scholarly journals Aspects of quantum information in finite density field theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Lucas Daguerre ◽  
Raimel Medina ◽  
Mario Solís ◽  
Gonzalo Torroba
Keyword(s):  
Field Theory ◽  
Quantum Information ◽  
Mutual Information ◽  
Fermi Surface ◽  
Relative Entropy ◽  
Chemical Potential ◽  
Operator Product ◽  
Dirac Fermions ◽  
Long Distance ◽  
Finite Density

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

INTERACTION OF MESOSCOPIC JOSEPHSON JUNCTION WITH A SUCCESSIVE SQUEEZED COHERENT FIELD

2000 ◽  
Vol 14 (16) ◽  
pp. 609-618
Author(s):  
V. A. POPESCU
Keyword(s):  
Coherent State ◽  
Josephson Junction ◽  
Coherent States ◽  
Quantum Noise ◽  
Shapiro Steps ◽  
Superconducting Ring ◽  
Coherent Field ◽  
Current Voltage ◽  
Quantum Current ◽  
The Difference

Signal-to-quantum noise ratio for quantum current in mesoscopic Josephson junction of a circular superconducting ring can be improved if the electromagnetic field is in a successive squeezed coherent state. The mesoscopic Josephson junctions can feel the difference between the successive squeezed coherent states and other types of squeezed coherent states because their current–voltage Shapiro steps are different. We compare our method with another procedure for superposition of two squeezed coherent states (a squeezed even coherent state) and consider the effect of different large inductances on the supercurrent.

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