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arXiv:1409.4647 · Physical Review E

Thermodynamics of creating correlations: Limitations and optimal protocols

David Edward Bruschi, Martí Perarnau-Llobet, Nicolai Friis, Karen V. Hovhannisyan, Marcus Huber

Published Mar 11, 2015• 69 citations
arXivHTMLPDF

Abstract

We establish a rigorous connection between fundamental resource theories at the quantum scale. Correlations and entanglement constitute indispensable resources for numerous quantum information tasks. However, their establishment comes at the cost of energy, the resource of thermodynamics, and is limited by the initial entropy. Here, the optimal conversion of energy into correlations is investigated. Assuming the presence of a thermal bath, we establish general bounds for arbitrary systems and construct a protocol saturating them. The amount of correlations, quantified by the mutual information, can increase at most linearly with the available energy, and we determine where the linear regime breaks down. We further consider the generation of genuine quantum correlations, focusing on the fundamental constituents of our universe: fermions and bosons. For fermionic modes, we find the optimal entangling protocol. For bosonic modes, we show that while Gaussian operations can be outperformed in creating entanglement, their performance is optimal for high energies.

DOI
10.1103/physreve.91.032118

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We establish a rigorous connection between fundamental resource theories at the quantum scale. Correlations and entanglement constitute indispensable resources for numerous quantum information tasks. However, their establishment comes at the cost of energy, the resource of thermodynamics, and is limited by the initial entropy. Here, the optimal conversion of energy into correlations is investigated. Assuming the presence of a thermal bath, we establish general bounds for arbitrary systems and construct a protocol saturating them. The amount of correlations, quantified by the mutual information, can increase at most linearly with the available energy, and we determine where the linear regime breaks down. We further consider the generation of genuine quantum correlations, focusing on the fundamental constituents of our universe: fermions and bosons. For fermionic modes, we find the optimal entangling protocol. For bosonic modes, we show that while Gaussian operations can be outperformed in creating entanglement, their performance is optimal for high energies.
We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement—the strongest form of entanglement in multipartite systems—can be created at any finite temperature when sufficiently many systems are considered. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamic considerations cannot be ignored.
Abstract Correlations lie at the heart of almost all scientific predictions. It is therefore of interest to ask whether there exist general limitations to the amount of correlations that can be created at a finite amount of invested energy. Within quantum thermodynamics such limitations can be derived from first principles. In particular, it can be shown that establishing correlations between initially uncorrelated systems in a thermal background has an energetic cost. This cost, which depends on the system dimension and the details of the energy-level structure, can be bounded from below but whether these bounds are achievable is an open question. Here, we put forward a framework for studying the process of optimally correlating identical (thermal) quantum systems. The framework is based on decompositions into subspaces that each support only states with diagonal (classical) marginals. Using methods from stochastic majorisation theory, we show that the creation of correlations at minimal energy cost is possible for all pairs of three- and four-dimensional quantum systems. For higher dimensions we provide sufficient conditions for the existence of such optimally correlating operations, which we conjecture to exist in all dimensions.
We consider physical situations where the resource theories of coherence and thermodynamics play competing roles. In particular, we study the creation of quantum coherence using unitary operations with limited thermodynamic resources. We find the maximal coherence that can be created under unitary operations starting from a thermal state and find explicitly the unitary transformation that creates the maximal coherence. Since coherence is created by unitary operations starting from a thermal state, it requires some amount of energy. This motivates us to explore the trade-off between the amount of coherence that can be created and the energy cost of the unitary process. We also find the maximal achievable coherence under the constraint on the available energy. Additionally, we compare the maximal coherence and the maximal total correlation that can be created under unitary transformations with the same available energy at our disposal. We find that when maximal coherence is created with limited energy, the total correlation created in the process is upper bounded by the maximal coherence, and vice versa. For two-qubit systems we show that no unitary transformation exists that creates the maximal coherence and maximal total correlation simultaneously with a limited energy cost.
The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost.
Abstract The presence of correlations in physical systems can be a valuable resource for many quantum information tasks. They are also relevant in thermodynamic transformations, and their creation is usually associated to some energetic cost. In this work, we study the role of correlations in the thermodynamic process of state formation in the single-shot regime, and find that correlations can also be viewed as a resource. First, we show that the energetic cost of creating multiple copies of a given state can be reduced by allowing correlations in the final state. We obtain the minimum cost for every finite number of subsystems, and then we show that this feature is not restricted to the case of copies. More generally, we demonstrate that in the asymptotic limit, by allowing a logarithmic amount of correlations, we can recover standard results where the free energy quantifies this minimum cost.
We study the energy exchange between two bosonic systems that interact via bilinear transformations in the mode operators. The first mode is considered as the thermodynamic system, while the second is regarded as the bath. This work finds its roots in a very recent formulation of quantum thermodynamics [Bera et al., Quantum 3, 121 (2019)] which allows one to consider baths that are not described by the usual Boltzmann-Gibbs canonical form. Baths can possess quantum properties, such as squeezing or coherence, and can be initially correlated with the system, even through entanglement. We focus mainly on the case of Gaussian states, by quantifying the relation between their defining parameters, namely the mean values of the quadratures and the covariance matrix, and relevant thermodynamical quantities such as the heat exchanged and the work performed during the interaction process. We fully solve the case of initially uncorrelated Gaussian states and provide the most general form of the first law of thermodynamics in this case. We also discuss the case of initially correlated states by considering a number of relevant examples, studying how correlations can assist some phenomena, e.g., work extraction or anomalous heat flows. Finally, we present an information-theoretic approach based on the Renyi entropy of order two for clarifying more generally the role of correlations on heat exchanges.