Generation of minimum energy entangled states

TL;DR

This paper explores methods to generate minimum energy bipartite entangled states in finite-dimensional systems, demonstrating that these states can be efficiently produced via specific unitaries or thermalization protocols, often at lower energy costs.

Contribution

It identifies explicit unitary operators and interaction terms for generating minimum energy entangled states, and compares their efficiency to other state generation methods.

Findings

Minimum energy entangled states can be generated with specific unitaries or thermalization.

Two of the three unitary transformations are easily implementable with local and nonlocal operations.

Generating minimum-energy states generally costs less energy than producing other entangled states.

Abstract

Quantum technologies exploiting bipartite entanglement could be made more efficient by using states having the minimum amount of energy for a given entanglement degree. Here, we study how to generate these states in the case of a bipartite system of arbitrary finite dimension either by applying a unitary transformation to its ground state or through a zero-temperature thermalization protocol based on turning on and off a suitable interaction term between the subsystems. In particular, we explicitly identify three possible unitary operators and five possible interaction terms. On one hand, two of the three unitary transformations turn out to be easily decomposable in terms of local elementary operations and a single nonlocal one, making their implementation easier. On the other hand, since the thermalization procedures can be easily adapted to generate many different states, we numerically show that, for each degree of entanglement, generating minimum-energy entangled states costs, in general, less than generating the vast majority of the other states.