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Heat Capacity and entanglement

Bruno Leggio

Published Oct 29, 2012• 0 citations
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Abstract

Starting from a recent result on thermodynamic equilibrium of quantum systems, a connection between thermal properties, originating from Gibbs state probabilistic structure, and quantum correlations is discussed as a consequence of entanglement monogamy. As an example, a simple two-qubit system is analyzed, allowing for an expression of such a connection as an explicit function linking heat capacity to a measure of bipartite entanglement.

DOI
10.1393/ncc/i2012-11311-9

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Starting from a recent result on thermodynamic equilibrium of quantum systems, a connection between thermal properties, originating from Gibbs state probabilistic structure, and quantum correlations is discussed as a consequence of entanglement monogamy. As an example, a simple two-qubit system is analyzed, allowing for an expression of such a connection as an explicit function linking heat capacity to a measure of bipartite entanglement.
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It is an established fact that quantum coherences have thermodynamic value. The natural question arises, whether other genuine quantum properties such as entanglement can also be exploited to extract thermodynamic work. In the present analysis, we show that the ergotropy can be expressed as a function of the quantum mutual information, which demonstrates the contributions to the extractable work from classical and quantum correlations. More specifically, we analyze bipartite quantum systems with locally thermal states, such that the only contribution to the egrotropy originates in the correlations. Our findings are illustrated for a two-qubit system collectively coupled to a thermal bath.
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The strong connection between correlations and quantum thermodynamics raises a natural question about the preparation of correlated quantum states from two copies of a thermal qubit. In this work we study the specific forms of allowed and forbidden bipartite correlations. As a consequence, we extend the result to separable but not absolutely separable class of product states. Preparation of a general form of entanglement from arbitrary thermal qubits is studied and, as an application, we propose a strategy to establish desired entanglement between two distant parties. The threshold temperature to produce entanglement from two copies of a thermal qubit has also been discussed from the resource theoretic perspective, which ensures that the bound on the temperature can be superseded with the help of a resource state. A dimension dependent upper bound on the temperature is derived, below which two copies of any d-dimensional thermal state can be entangled in 2×d dimensions.