Untangling Entanglement

Abstract

In this paper recent work that attempts to link quantum entanglement to (i) thermodynamic energy, (ii) thermodynamic entropy and (iii) information is reviewed. With respect to the first two links the paper is essentially expository. The final link is elaborated on: it is argued that the value of the entanglement of a bipartite system in a pure state is equal to the value of the irreducible uncertainty (i.e. irreducibly missing information) about its subsystems and that this suggests that entanglement gives rise to irreducible uncertainty. (The exact meaning of the phrase "irreducible uncertainty", as used here, is explained in the body of the paper. Roughly speaking, it is the uncertainty about the postmeasurement state of a system that cannot be removed at the pre-measurement stage.) This analysis is used to make a further connection between entanglement and statistical mechanical entropy: it is argued that these properties are indirectly linked, in so far as both give rise to forms of uncertainty (albeit rather different forms of uncertainty about rather different things).

On the Relationship between Entropy and Information.

“…In some other efforts, much work has been done on the relation of entropy and information in recent years. Yet, most of the authors think over the thermodynamic systems either under a quantum regime [16,17,18] or in the context of a quantum entanglement with a bath [19,20,21,22]. A dominant presumption in all these works is that during the change of state of the system, there is no material change.…”