Thermodynamic cost of creating correlations

Abstract

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.

Quantum thermodynamics

“…[52][53][54][55][56][57][58][59], for a variety of settings, including unitary and non-unitary processes. For example, the thermodynamic efficiency of an engine operating on pairs of correlated atoms can be quantified in terms of quantum discord and it was shown to exceed the classical efficiency value [54].…”

“…In [60] the minimal heat dissipation for coupling a harmonic oscillator that starts initially in local thermal equilibrium, and ends up correlated with a bath of harmonic oscillators in a global thermal equilibrium state, is determined and it was shown that this heat contribution resolves a previously reported second law violation. Thermodynamic aspects of creating correlations are also studied in [59] where the minimum work cost is established for unitarily evolving an initial, locally thermal, state of N systems to a global correlated state. A maximum temperature is derived at which entanglement can still be created, along with the minimal associated energy cost.…”

“…Finally, we point out that time has an important role to play in engine performance, since it relates to power. As detailed in 6.7, both coherence and time play important roles in the design of quantum machines [58,59,181]. As an example, consider that the evolution of an initial state to a final state cannot happen faster than a fundamental bound that depends on the Hamiltonian and states involved.…”

“…This role relates to storing work in correlations. It has been shown by several authors [58,59,191] that measures of correlations like quantum mutual information and entanglement can affect the performance of thermal machines.…”

Maximally genuine multipartite entangled mixed X-states ofN-qubits

“…However, as recently shown by Huber et al [41], N-qubit thermal states of arbitrarily high temperatures and N sufficiently large (represented, in the computational basis, by diagonal density matrices arbitrarily close to the identity, hence fulfilling (28)) can acquire GM-entanglement by means of rotations to Dicke-like (non-X) states, thus providing a counter-example to the original conjecture.…”