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arXiv:2010.13644 · Physical Review A

Generation of minimum-energy entangled states

Nicolò Piccione, Benedetto Militello, Anna Napoli, Bruno Bellomo

Published Jun 1, 2021• 5 citations
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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.

DOI
10.1103/physreva.103.062402

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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.
We investigate the minimum entanglement cost of the deterministic implementation of two-qubit controlled-unitary operations using local operations and classical communication (LOCC). We show that any such operation can be implemented by a three-turn LOCC protocol, which requires at least 1 ebit of entanglement when the resource is given by a bipartite entangled state with Schmidt number 2. Our result implies that there is a gap between the minimum entanglement cost and the entangling power of controlled-unitary operations. This gap arises due to the requirement of implementing the operations while oblivious to the identity of the inputs.
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The study of entanglement between bosonic systems is of primary importance for establishing feasible resources needed for implementing quantum information protocols, both in their interacting atomic or photonic realizations. Atomic systems are particularly efficient in the production of large amounts of entanglement, providing higher information density than conventional qubit entangled states. Such increased quantum resources pave the way to novel fundamental tests of nature and efficient applications in quantum information, metrology and sensing. We consider a basic setup made up of two parties A and B, each one populated by a single level bosonic variable. The bosons are interacting and can hop between A and B, thus describing a two-site Bose-Hubbard Hamiltonian. We consider the generation of quantum states in several situations that cover the majority of physical realizations: ground state, finite temperature, unitary dynamics, dissipation through dephasing and loss of particles. The system is analyzed through truncated exact diagonalization, as a function of the microscopic parameters. The nonseparability of the obtained quantum states is estimated by means of the negativity, which has recently been proven to be a suitable measure of entanglement [M. Roncaglia, A. Montorsi and M. Genovese, Phys. Rev. A90 (2014) 062303]. Finally, we calculate lower bounds of the entanglement of formation (EOF), an indicator that quantifies the minimal amount of entanglement resources needed to build up such states.
We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing entanglement entropy ΔS , by a product state, and we show how to construct modes achieving this minimal energy cost. Thus, we obtain a protocol independent lower bound on the extraction of pure state entanglement from quadratic systems. Due to their generality, our results apply to a large range of physical systems, as we discuss with examples.