Entanglement fluctuation theorems

TL;DR

This paper introduces entanglement fluctuation theorems showing that reversible entanglement transformations are possible on individual systems with fluctuating entanglement, linking quantum information theory with thermodynamic fluctuation relations.

Contribution

It derives necessary and sufficient conditions for entanglement manipulation with fluctuations and introduces an entanglement battery to enable optimal protocols, connecting quantum entanglement with thermodynamic principles.

Findings

Reversible entanglement transformations can be performed on single systems with fluctuating entanglement.

Derived an entanglement fluctuation equation analogous to the Jarzynski equality.

Established relations between entanglement manipulation and thermodynamic laws.

Abstract

Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.