Quantum Correlation without Classical Correlations

Abstract

We show that genuine multiparty quantum correlations can exist on its own, without a supporting background of genuine multiparty classical correlations, even in macroscopic systems. Such possibilities can have important implications in the physics of quantum information and phase transitions.Quantum and classical correlations lie at the heart of sciences and technologies. The emerging quantum technology crucially depends on correlations that are different and more subtle than the ones in classical physics. This quantum form of correlations, known as entanglement [1], is currently being exploited to achieve higher levels of security in cryptography [2] and faster rates of information processing in computers [3]. Since quantum physics contains the classical one as a special case, we may think that reducing entanglement will in the same way ultimately lead to the reduction of all correlations to classical correlations. We will however show that this intuition is completely false; surprisingly, genuine multiparty entanglement can exist on its own without the need of genuine multiparty classical correlations, even for macroscopic systems. This result has potentially fundamental implications in the physics of quantum information and phase transitions, and in the current characterization of the quantum to classical transition.It is widely known that quantum correlations are of a different kind than classical ones, and that quantum correlations can be vanishing even when classical correlations are present. However, the fact that even the opposite is true has so far eluded us. We present a general method to obtain that multiparty quantum and classical correlations are independent for a certain class of multiparty states, shared between an arbitrary odd number of two-dimensional systems (qubits). This phenomenon cannot happen for quantum systems with two subsystems; neither can it happen for pure multiparty states.Quantum and classical correlations. We begin by discussing in generality how to distinguish quantum correlations and specifically genuine multiparty correlations, as well as the analogous classical notions. For an n-party state ρ, it is established usage to call it separable (or, precisely, fully separable) if it is a probability mixture (i.e., convex combination) of n-party product states [4]; otherwise the state is (somehow) entangled. A more stringent notion is that of genuine n-party entanglement [5], which demands that the state is not in the convex hull of tensor products over any bipartition of the n systems. [See [5] for a whole hierarchy of notions, k-separability and the complement, genuine (n + 2 − k)-party entanglement, for k = 2, . . . , n.]All this is fairly canonical -though one might consider the idea of defining quantum correlations via the violation of some Bell inequality [6], which is a strictly different concept, already in the bipartite case [4,7]. We shall come back to this issue, but for the present paper, we stick with this more encompassing notion. On the other hand, defining correlati...

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