Locally inaccessible information as a fundamental ingredient to quantum information

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformation-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

show abstract

“…Finally, (Fanchini et al, 2012) give the discord chain rule, which expresses entanglement of formation in terms of different discords:…”

Section: Conservation Lawmentioning

confidence: 99%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

View full text Add to dashboard Cite

show abstract

“…To define an invariant quantity and an essential measure of the global gain in the triple, we use the sum of the distinct EOF tangles. To calculate the sum of the EOF tangles, we use the notation in terms of the flow of quantum correlation [11], defined as…”

Section: Permutation-invariant Tangle and Applicationsmentioning

confidence: 99%

Why entanglement of formation is not generally monogamous

et al. 2013

View full text Add to dashboard Cite

Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system A is maximally entangled with another system B, it cannot be entangled at all with a third system C. This concept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pair BC can be divided as contributions of the entanglement between A and B and A and C, plus a term τ ABC involving genuine tripartite entanglement and so expected to be always positive. A very important measure in quantum information theory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become a monogamous measure, i.e., for τ ABC 0. The relation derived is connected to the discrepancy between quantum and classical correlations, τ ABC being negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglement measure that is always monogamous.

show abstract

“…Actually, for a tripartite pure state it is always possible to infer the EOF and the QD if just one of the possible bipartitions is known. Moreover, the quantum discord between A and E can be calculated analytically without any approximation [23].…”

Section: Quantum Correlations Between One Atom and The Environmentmentioning

confidence: 99%

Quantum correlations between each qubit in a two-atom system and the environment in terms of interatomic distance

2012

View full text Add to dashboard Cite

The quantum correlations between a qubit and its environment are described quantitatively in terms of interatomic distance. Specifically, considering a realistic system of two two-level atoms and taking into account the dipole-dipole interaction and collective damping, the quantum entanglement and quantum discord are investigated during the dissipative process as functions of the interatomic distance. For atoms that are initially maximally entangled, it turns out that there is a critical distance at which each atom is maximally quantum correlated with its environment. Counterintuitively, the approach of the two atoms can maximize the entanglement between each one and the environment and, even at the same distance, minimize the loss of entanglement between the pair.

show abstract

Locally inaccessible information as a fundamental ingredient to quantum information

Cited by 47 publications

References 35 publications

The classical-quantum boundary for correlations: Discord and related measures

The classical-quantum boundary for correlations: Discord and related measures

Why entanglement of formation is not generally monogamous

Quantum correlations between each qubit in a two-atom system and the environment in terms of interatomic distance

Contact Info

Product

Resources

About