Energy bounds for entangled states

Abstract

We find the minimum and the maximum value for the local energy of an arbitrary finite bipartite system for any given amount of entanglement, also identifying families of states reaching these bounds and sharing formal analogies with thermal states. Then, we numerically study the probability of randomly generating pure states close to these energy bounds finding, in all the considered configurations, that it is extremely low except for the two-qubit and highly degenerate cases. These results can be important in quantum technologies to design energetically more efficient protocols.

Generation of minimum energy entangled states

“…In Ref. [19] we showed that, for a given degree of entanglement E, the states minimizing the average of H 0 are pure states of the form…”

“…More details about all these facts are given in Ref. [19]. The aim of this paper is to present possible strategies to generate states of the form of Eq.…”

“…Accordingly, the study of suitable protocols to generate entangled states in a great variety of physical setups has attracted much attention in the last decades [5][6][7][8][9][10][11][12][13][14][15][16]. However, generating quantum states with a certain amount of entanglement usually requires converting other resources into it, such as coherence [17,18], non-equilibrium thermal resources [18], and energy [19]. Among these resources, energy is one of the most important with regard to the evaluation of the generation cost.…”

“…Among these resources, energy is one of the most important with regard to the evaluation of the generation cost. Recently, some studies dealt with the energy cost of quantum operations [20], including the generation of correlations [21] and entanglement [19,[22][23][24]. In particular, in Ref.…”

“…In particular, in Ref. [19] we found the bounds on the local energy of a bipartite system of arbitrary finite dimension imposed by having a certain amount of entanglement. Moreover, we have also identified the states saturating these bounds.…”