Oblique discord

2017 ◽  
Vol 31 (02) ◽  
pp. 1650256
Author(s):  
Jianwei Xu
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Orthonormal Basis ◽  
Quantum Correlations ◽  
Information Theoretic ◽  
Separable States ◽  
Geometric Measure ◽  
Definition Of

Discord and entanglement characterize two kinds of quantum correlations, and discord captures more correlation than entanglement in the sense that even separable states may have nonzero discord. In this paper, we propose a new kind of quantum correlation that we call as oblique discord. A zero-discord state corresponds to an orthonormal basis, while a zero-oblique-discord state corresponds to a basis which is not necessarily orthogonal. Under this definition, the set of zero-discord states is properly contained inside the set of zero-oblique-discord states, and the set of zero-oblique-discord states is properly contained inside the set of separable states. We give a characterization of zero-oblique-discord states via quantum mapping, provide a geometric measure for oblique discord, and raise a conjecture, which if it holds, then we can define an information-theoretic measure for oblique discord. Also, we point out that the definition of oblique discord can be properly extended to some different versions just as the case of quantum discord.

Improvement of quantum correlations by repetitive quantum error correction

2019 ◽  
Vol 17 (05) ◽  
pp. 1950044
Author(s):  
A. El Allati ◽  
H. Amellal ◽  
A. Meslouhi
Keyword(s):  
Error Correction ◽  
Quantum Correlation ◽  
Coherent States ◽  
Quantum Discord ◽  
Error Correcting Code ◽  
Quantum Correlations ◽  
Quantum Error Correction ◽  
Optical Field ◽  
Quantum Error ◽  
Entangled Coherent States

A quantum error-correcting code is established in entangled coherent states (CSs) with Markovian and non-Markovian environments. However, the dynamic behavior of these optical states is discussed in terms of quantum correlation measurements, entanglement and discord. By using the correcting codes, these correlations can be as robust as possible against environmental effects. As the number of redundant CSs increases due to the repetitive error correction, the probabilities of success also increase significantly. Based on different optical field parameters, the discord can withstand more than an entanglement. Furthermore, the behavior of quantum discord under decoherence may exhibit sudden death and sudden birth phenomena as functions of dimensionless parameters.

QUANTUM CORRELATIONS IN THE ENTANGLEMENT DISTILLATION PROTOCOLS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350029
Author(s):  
SHAO-XIONG WU ◽  
JUN ZHANG ◽  
CHANG-SHUI YU ◽  
HE-SHAN SONG
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Entangled States ◽  
Entanglement Distillation

We study the quantum correlations between source and target pairs in different protocols of entanglement distillation of one kind of entangled states. We find that there does not exist any quantum correlation in the standard recurrence distillation protocol, while quantum discord and even quantum entanglement are always present in the other two cases of the improved distillation protocols. In the three cases, the distillation efficiency improved with the quantum correlations enhanced.

QUANTUM CORRELATIONS IN THE "q-DEFORMED" WERNER STATE

2013 ◽  
Vol 11 (02) ◽  
pp. 1350018 ◽  
Author(s):  
BO LIU ◽  
KANG XUE ◽  
GANGCHENG WANG ◽  
CHUNFANG SUN ◽  
LIDAN GOU ◽  
...  
Keyword(s):  
Quantum Discord ◽  
Singlet State ◽  
Great Influence ◽  
Quantum Correlations ◽  
Werner State ◽  
Single Loop ◽  
Geometric Measure ◽  
Topological Parameter ◽  
Spin Singlet ◽  
Two Parameters

We investigate quantum discord of the "q-deformed" Werner state via Yang–Baxterization approach. There are two parameters q and u in this "q-deformed" Werner state. The parameter u, which plays an important role in some typical models, is related to the probability of the "q-deformed" two-qubit spin singlet state in this study. The "q-deformed" parameter q is related to the single loop through d = q + q-1. When topological parameter d approaches 2 (i.e. q → 1), the "q-deformed" Werner state degenerates into the well-known Werner state. The results show that topological parameter d has great influence on quantum correlations of the "q-deformed" Werner state. When we fix the parameter u, the quantum correlations decrease with increasing the single loop d. When d approaches +∞ (i.e. q → 0+ or +∞), quantum discord, geometric measure of quantum discord and entanglement all tend to 0. While d approaches 2 (i.e. q → 1), all of them just have the same results with the Werner state.

THERMAL DISCORD AND NEGATIVITY IN A TWO-SPIN-QUTRIT SYSTEM UNDER DIFFERENT MAGNETIC FIELDS

2013 ◽  
Vol 11 (08) ◽  
pp. 1350070 ◽  
Author(s):  
XIAO-JING LI ◽  
HUI-HUI JI ◽  
XI-WEN HOU
Keyword(s):  
Magnetic Fields ◽  
Quantum Discord ◽  
Strong Field ◽  
Quantum Correlations ◽  
Mixed States ◽  
Classical Correlation ◽  
Lower Temperature ◽  
Qubit States ◽  
Quantum And Classical Correlations

The characterization of quantum discord (QD) has been well understood only for two-qubit states and is little known for mixed states beyond qubits. In this work, thermal quantum discord is studied for a qutrit system in different magnetic fields, where classical correlation and entanglement negativity are calculated for comparison. It is shown that the discord is more robust against temperature than the negativity. For a suitable region of magnetic field and its direction, the discord is non-zero while the negativity is zero. When the system is at a lower temperature, these three quantities, however, display a similar behavior for the varied field and direction, and their discontinuities come from crossovers between different ground states in the system. Moreover, the inequality between the quantum and classical correlations depends upon the system parameters as well as the temperature. In particular, both correlations are equal at a suitable field, direction, and temperature. Remarkably, such an equality remains for a strong field in the antiparallel direction, while both correlations in two-qubit systems are identical for any antiparallel field and temperature. These are useful for quantum information and understanding quantum correlations in qutrit mixed states.

scholarly journals Geometric measures of discordlike quantum correlations based on Tsallis relative entropy

2019 ◽  
Vol 17 (04) ◽  
pp. 1950034
Author(s):  
Weijing Li
Keyword(s):  
Relative Entropy ◽  
Quantum Correlation ◽  
Quantum Correlations ◽  
Partial Coherence ◽  
Good Measure ◽  
Coherence Measure ◽  
Geometric Measure ◽  
Special Cases ◽  
Analytic Expression ◽  
Correlation Measures

A kind of new geometric measure of quantum correlations is formulated. The proposed formulation is in terms of the quantum Tsallis relative entropy and can naturally be viewed as a one-parameter extension quantum discordlike measure that satisfies all requirements of a good measure of quantum correlations. It is of an elegant analytic expression and contains several existing good quantum correlation measures as special cases. The partial coherence measure is also investigated.

Robustness of Quantum Correlations in Entangled Two su(2) Systems Non-mutually Interacting with su(1, 1) System under Intrinsic Decoherence

2018 ◽  
Vol 25 (03) ◽  
pp. 1850015
Author(s):  
A.-B. A. Mohamed ◽  
M. S. Abdalla ◽  
A.-S. F. Obada
Keyword(s):  
Steady State ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Bell State ◽  
Analytical Description ◽  
Quantum Correlations ◽  
Total System ◽  
Intrinsic Decoherence ◽  
Geometric Quantum Discord ◽  
Phase Decoherence

Two two-level systems generated by su(2) algebra are initially prepared in a maximum nonsymmetric Bell state and having no mutual interaction. Each su(2)-system spatially interacts with two-mode cavity field in the nondegenerate parametric amplifier type cast through operators governed by su(1, 1) Lie algebra. An analytical description for the time evolution of the final state of the total system with the effect of intrinsic decoherence is found. Therefore, the robustness of the quantum correlations between the two su(2)-system is investigated by means of geometric quantum discord, measurement-induced nonlocality and negativity. We analyze in some detail the influence of initial coherence intensities, detuning and phase decoherence parameters on the steady-state correlation. We find that the steady-state correlations can be generated and enhanced by controlling the parameters of: the initial coherence intensities, the Bargmman index and the detuning. It is shown that the phenomenon of sudden death and re-birth of entanglement, and the sudden changes of the geometric quantum correlation can be controlled by these parameters. We find that the robustness of the quantum correlation can be greatly enhanced by the Bargmman index and the resonance detuning. Negativity is the measure most susceptible to phase decoherence, while geometric quantum discord and measurement-induced nonlocality are the more robust measures.

MONOGAMY PROPERTIES OF QUANTUM DISCORD FOR A THREE-QUBIT ENTANGLED STATE

2013 ◽  
Vol 27 (07) ◽  
pp. 1350049 ◽  
Author(s):  
XUE-KE SONG ◽  
TAO WU ◽  
LIU YE
Keyword(s):  
Relative Entropy ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Numerical Calculations ◽  
Entangled State ◽  
Geometric Quantum Discord ◽  
The Given

In this paper, we obtain the pairwise quantum discord for a three-qubit W-class state, and investigate the monogamy property of quantum discord by two different ways (relative entropy-based distance and geometric square-norm distance). Through numerical calculations, we find that a party cannot have maximal quantum correlations with the other two parties simultaneously. For the given state, the quantum correlation between particles 1 and 3 induces limitation on the quantum correlation between them and particle 2. Moreover, the result also shows that the geometric quantum discord of the given W-class state obeys the monogamy property while the entropy quantum discord violates.

scholarly journals Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 785 ◽  
Author(s):  
Iulia Ghiu ◽  
Roberto Grimaudo ◽  
Tatiana Mihaescu ◽  
Aurelian Isar ◽  
Antonino Messina
Keyword(s):  
Time Evolution ◽  
Quantum Correlation ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Initial State ◽  
Analytical Treatment ◽  
Werner State ◽  
Driven System ◽  
Physical Reasons

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.

scholarly journals Quantum Reactivity: An Indicator of Quantum Correlation

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 6
Author(s):  
Shahabeddin M. Aslmarand ◽  
Warner A. Miller ◽  
Verinder S. Rana ◽  
Paul M. Alsing
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Triangle Inequality ◽  
Singlet State ◽  
Higher Dimensions ◽  
Quantum Correlations ◽  
Information Geometry ◽  
Quantum Systems ◽  
Geometric Quantity ◽  
Higher Dimensional

Geometry is often a valuable guide to complex problems in physics. In this paper, we introduce a novel geometric quantity called quantum reactivity (QR) to probe quantum correlations in higher-dimensional quantum systems. Much like quantum discord, QR is not a measure of quantum entanglement but can be useful in quantum information processes where a notion of quantum correlation in higher dimensions is needed. Both quantum discord and QR are extendable to an arbitrarily large number of qubits; however, unlike discord, QR satisfies the invariance under unitary operations. Our approach parallels Schumacher’s singlet state triangle inequality, which used an information geometry-based entropic distance. We use a generalization of information distance to area, volume, and higher-dimensional volumes and then use these to define a quantity that we call QR, which is the familiar ratio of surface area to volume. We examine a spectrum of multipartite states (Werner, W, GHZ, randomly generated density matrices, etc.) and demonstrate that QR can provide an ordering of these quantum states as to their degree of quantum correlation.

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