We report opposite statistical-mechanical behaviors of the two major paradigms in which quantum correlation measures are defined, viz., the entanglement-separability paradigm and the information-theoretic one. We show this by considering the ergodic properties of such quantum correlation measures in transverse quantum $XY$ spin- $\frac{1}{2}$ systems in low dimensions. While entanglement measures are ergodic in such models, the quantum correlation measures defined from an information-theoretic perspective can be nonergodic.We report opposite statistical-mechanical behaviors of the two major paradigms in which quantum correlation measures are defined, viz., the entanglement-separability paradigm and the information-theoretic one. We show this by considering the ergodic properties of such quantum correlation measures in transverse quantum $XY$ spin-$\frac{1}{2}$ systems in low dimensions. While entanglement measures are ergodic in such models, the quantum correlation measures defined from an information-theoretic perspective can be nonergodic.

arXiv:1112.1856Physical Review AJul 30, 201213 citations

Quantum Coherence and Quantum Correlations

Gerard J. Machado

Jul 9, 20170 citations

Dual entanglement measures based on no local cloning and no local deleting

Michał Horodecki, Aditi Sen, Ujjwal Sen

The impossibility of cloning and deleting of unknown states constitute important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However, if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local cloning and no local deleting. The measures are relative entropy distances of the desired states in a (generally impossible) perfect local cloning or local deleting process from the best approximate state that is actually obtained by imperfect local cloning or deleting machines. Just like the dual measures of entanglement cost and distillable entanglement, the proposed measures are based on important processes in quantum information. We discuss their properties. For the case of pure states, estimations of these two measures are also provided. Interestingly, the entanglement of cloning for a maximally entangled state of two two-level systems is not unity.The impossibility of cloning and deleting of unknown states constitute important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However, if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local cloning and no local deleting. The measures are relative entropy distances of the desired states in a (generally impossible) perfect local cloning or local deleting process from the best approximate state that is actually obtained by imperfect local cloning or deleting machines. Just like the dual measures of entanglement cost and distillable entanglement, the proposed measures are based on important processes in quantum information. We discuss their properties. For the case of pure states, estimations of these two measures are also provided. Interestingly, the entanglement of cloning for a maximally entangled state of two two-level systems is not unity.

arXiv:quant-ph/0403169Physical Review ANov 29, 200420 citations

Measuring correlations in quantum systems

Daniel Manzano

Mar 31, 20190 citations

Multipartite optimized correlation measures and holography

Oliver Dewolfe A, Joshua Levin, Graeme Smith

We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced $Q$ correlation and $R$ correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and the recently introduced $Q$ correlation and $R$ correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.

arXiv:2007.11587Physical review. D/Physical review. D.Sep 8, 20207 citations

XY

spin-

\frac{1}{2}

systems in low dimensions. While entanglement measures are ergodic in such models, the quantum correlation measures defined from an information-theoretic perspective can be nonergodic.

Q

correlation and

R

correlation. Some correlation measures vanish only on product states and, thus, quantify both classical and quantum correlations; others vanish on any separable state, capturing quantum correlations alone. We then use a procedure motivated by the surface-state correspondence to construct holographic duals for the correlation measures as linear combinations of bulk surfaces. The geometry of the surfaces can preserve, partially break, or fully break the symmetry of the correlation measure. The optimal purification is encoded in the locations of certain points, whose locations are fixed by constraints on the areas of combinations of surfaces. This gives a new concrete connection between information theoretic quantities evaluated on a boundary state and detailed geometric properties of its dual.