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.

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 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.

scholarly journals FROZEN DISCORD IN NON-MARKOVIAN DEPHASING CHANNELS

2011 ◽  
Vol 09 (03) ◽  
pp. 981-991 ◽  
Author(s):  
LAURA MAZZOLA ◽  
JYRKI PIILO ◽  
SABRINA MANISCALCO
Keyword(s):  
Hilbert Space ◽  
Colored Noise ◽  
Geometric Interpretation ◽  
Quantum Decoherence ◽  
Initial State ◽  
Memory Kernel ◽  
Single Qubit ◽  
Classical State ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

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.

scholarly journals Quantum and Classical Correlations in Waveguide Lattices

2009 ◽  
Vol 102 (25) ◽  
Author(s):  
Yaron Bromberg ◽  
Yoav Lahini ◽  
Roberto Morandotti ◽  
Yaron Silberberg
Keyword(s):  
Classical Correlations ◽  
Quantum And Classical Correlations
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