scholarly journals Criteria for measures of quantum correlations

2012 ◽  
Vol 12 (9&10) ◽  
pp. 721-742
Author(s):  
Aharon Brodutch ◽  
Kavan Modi
Keyword(s):  
Quantum Discord ◽  
Quantum Correlations ◽  
Good Measure ◽  
General Mechanism ◽  
Mixed States ◽  
Entanglement Measures ◽  
Measurement Basis ◽  
Important Quality ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Entanglement does not describe all quantum correlations and several authors have shown the need to go beyond entanglement when dealing with mixed states. Various different measures have sprung up in the literature, for a variety of reasons, to describe bipartite and multipartite quantum correlations; some are known under the collective name {\it quantum discord}. Yet, in the same sprit as the criteria for entanglement measures, there is no general mechanism that determines whether a measure of quantum and classical correlations is a proper measure of correlations. This is partially due to the fact that the answer is a bit muddy. In this article we attempt tackle this muddy topic by writing down several criteria for a ``good" measure of correlations. We breakup our list into \emph{necessary}, \emph{reasonable}, and \emph{debatable} conditions. We then proceed to prove several of these conditions for generalized measures of quantum correlations. However, not all conditions are met by all measures; we show this via several examples. The reasonable conditions are related to continuity of correlations, which has not been previously discussed. Continuity is an important quality if one wants to probe quantum correlations in the laboratory. We show that most types of quantum discord are continuous but none are continuous with respect to the measurement basis used for optimization.

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 Correlations in geometric states

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Wu-zhong Guo
Keyword(s):  
Central Charge ◽  
Convex Combination ◽  
Vacuum State ◽  
Quantum Correlations ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Classical Geometry ◽  
Accessible Information ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Abstract In this paper we explore the correlations in the geometric states. Here the geometric state means the state in CFTs that can be effectively described by classical geometry in the bulk in the semi-classical limit G → 0. By using the upper bound of Holevo information we show the convex combination of geometric states cannot be a geometric state. To understand the duality between thermofield double state and eternal black hle, we construct several correlated states of two CFTs. In all the examples we show their correlations are too weak to produce the a connected spacetime. Then we review the measure named quantum discord and use it to characterize the classical and quantum correlations in quantum field theories. Finally, we discuss the correlations between two intervals A and B with distance d in the vacuum state of 2D CFTs with large central charge c. The feature is the phase transition of the mutual information I (ρAB). We analyse the quasi-product state of ρAB for large d. By using the Koashi-Winter relation of tripartite states the quantum and classical correlations between A and B can expressed as Holevo information, which provides a new understanding of the correlations as accessible information.

Adiabatic demagnetization at absolute negative temperature: Generation of quantum correlations

2019 ◽  
Vol 17 (03) ◽  
pp. 1950023
Author(s):  
Gregory B. Furman ◽  
Shaul D. Goren ◽  
Victor M. Meerovich ◽  
Vladimir L. Sokolovsky
Keyword(s):  
Magnetic Field ◽  
Negative Temperature ◽  
Quantum Correlations ◽  
Zero Magnetic Field ◽  
Positive Temperature ◽  
Nuclear Spins ◽  
Adiabatic Demagnetization ◽  
Negative Temperatures ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

In this paper, we study behavior of the correlations, both quantum and classical, under adiabatic demagnetization process in systems of nuclear spins with dipole–dipole interactions in an external magnetic field and in the temperature range including positive and negative temperatures. For a two-spin system, analytical expressions for the quantum and classical correlations are obtained. It is revealed that the field dependences of the quantum and classical correlations at positive and negative temperatures are substantially different. This difference most clearly appears in the case of zero magnetic field: at negative temperature, the measures of quantum correlations tend to the maximum values with a temperature increase. At positive temperature, these quantities tend to zero at a decrease of magnetic field. It is also found that, for the nearest-neighboring spins in the same field, the values of concurrence and discord are larger at negative temperatures than at positive ones.

scholarly journals Entanglement, Purity, and Information Entropies in Continuous Variable Systems

2005 ◽  
Vol 12 (02) ◽  
pp. 189-205 ◽  
Author(s):  
Gerardo Adesso ◽  
Alessio Serafini ◽  
Fabrizio Illuminati
Keyword(s):  
Tomographic Reconstruction ◽  
Continuous Variable ◽  
The State ◽  
Upper And Lower Bounds ◽  
Mixed States ◽  
Gaussian States ◽  
Pure States ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.

scholarly journals THE BALANCE OF QUANTUM CORRELATIONS FOR A CLASS OF FEASIBLE TRIPARTITE CONTINUOUS VARIABLE STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345024 ◽  
Author(s):  
STEFANO OLIVARES ◽  
MATTEO G. A. PARIS
Keyword(s):  
Conservation Laws ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Noisy Environment ◽  
Mixed States ◽  
Von Neumann ◽  
Entanglement Of Formation ◽  
Pure States ◽  
Gaussian Quantum Discord

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi–Winter-like conservation laws involving Gaussian entanglement of formation (EoF), Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.

scholarly journals QUANTUM DISCORD AND QUANTUM COMPUTING — AN APPRAISAL

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1787-1805 ◽  
Author(s):  
ANIMESH DATTA ◽  
ANIL SHAJI
Keyword(s):  
Quantum Computing ◽  
Computational Complexity ◽  
Complexity Theory ◽  
Quantum Discord ◽  
Primary Motivation ◽  
Classical Simulation ◽  
Classical Correlations ◽  
Quantum And Classical Correlations ◽  
Theory Lead

We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of non-classical advantages in computation. Completeness results from computational complexity theory lead to the identification of very disparate problems, and offer a kaleidoscopic view into the realm of quantum enhancements in computation. Emphasis is placed on the "power of one qubit" model, and the boundary between quantum and classical correlations as delineated by quantum discord. A recent result by Eastin on the role of this boundary in the efficient classical simulation of quantum computation is discussed. Perceived drawbacks in the interpretation of quantum discord as a relevant certificate of quantum enhancements are addressed.

Time evolution of quantum correlations in superconducting flux-qubits under classical noises

2017 ◽  
Vol 15 (02) ◽  
pp. 1750015 ◽  
Author(s):  
Tchoffo Martin ◽  
Tsamouo Tsokeng Arthur ◽  
Fouokeng Georges Collince ◽  
Lukong Cornelius Fai
Keyword(s):  
Quantum Discord ◽  
Energy Levels ◽  
Quantum Correlations ◽  
Noise Spectrum ◽  
Entanglement Witnesses ◽  
Entanglement Measures ◽  
Flux Qubits ◽  
Common Coupling ◽  
Flux Qubit ◽  
Markovian Regime

We analyze the dynamics of both entanglement and quantum discord (QD) in a system of two non-interacting flux-qubits initially prepared in a Bell's state and subjected to either static or random telegraph noises (RTNs). Both independent and common sources of system-environment coupling are considered either in the Markovian or non-Markovian regime and the results are compared to those of ordinary qubits. Under suitable conditions, both entanglement and QD are more robust in flux-qubit systems than classical ones. In the Markovian regime where the decay is monotonic, they are both stronger in different environment coupling than in common coupling, while the opposite is found in the non-Markovian regime where the dynamics is stressed by sudden death and revival phenomena, more robust in qubits than in flux-qubits under dynamical RTN. Weakness of revival amplitudes is interpreted as a noise spectrum-related induced interaction affecting quantum features of the system, while energy level non-degeneracy (at zero-splitting) of flux-qubits induces a phase factor that set conditions under which entangled states can be experimentally witnessed in flux-qubit systems. Note that the energy levels non-degeneracy has no particular effect on other entanglement measures apart from entanglement witnesses.

scholarly journals Correlations in Two-Qubit Systems under Non-Dissipative Decoherence

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 20
Author(s):  
Diego G. Bussandri ◽  
Tristán M. Osán ◽  
Pedro W. Lamberti ◽  
Ana P. Majtey
Keyword(s):  
Mutual Information ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Standard Quantum ◽  
Optimal Value ◽  
Quantum Mutual Information ◽  
Classical Correlations ◽  
Correlation Measures ◽  
Qubit States

We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.

Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states

2019 ◽  
Vol 16 (07) ◽  
pp. 1950109
Author(s):  
Fatima-Zahra Siyouri ◽  
Hicham Ait Mansour ◽  
Fadoua Elbarrichi
Keyword(s):  
Wigner Function ◽  
Quantum Discord ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Qubit System ◽  
Classical Correlations ◽  
Werner States ◽  
System F

We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.

scholarly journals Pairwise quantum and classical correlations in multi-qubits states via linear relative entropy

2014 ◽  
Vol 12 (06) ◽  
pp. 1450035 ◽  
Author(s):  
M. Daoud ◽  
R. Ahl Laamara ◽  
H. El Hadfi
Keyword(s):  
Relative Entropy ◽  
Qubit State ◽  
Mixed States ◽  
Special Cases ◽  
Pairwise Correlations ◽  
Classical Correlations ◽  
Additivity Relation ◽  
Quantum And Classical Correlations ◽  
Explicit Expressions

The pairwise correlations in a multi-qubit state are quantified through a linear variant of relative entropy. In particular, we derive the explicit expressions of total, quantum and classical bipartite correlations. Two different bi-partioning schemes are considered. We discuss the derivation of closest product, quantum–classical and quantum–classical product states. We also investigate the additivity relation between the various pairwise correlations existing in pure and mixed states. As illustration, some special cases are examined.

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