Correspondence between maximally entangled states in discrete and Gaussian regimes

TL;DR

This paper explores a correspondence between discrete and Gaussian quantum states, demonstrating that Gaussian maximally entangled states are more suitable for quantum information tasks than traditional two-mode squeezed vacuum states.

Contribution

It introduces a comparison framework between discrete maximally entangled states and Gaussian maximally entangled states using quantum fidelity calculations.

Findings

Gaussian maximally entangled states are more suitable for quantum information tasks.

Explicit fidelity calculations compare discrete and Gaussian entangled states.

Gaussian maximally entangled states outperform TMSV states in certain regimes.

Abstract

We study a general corresponding principle between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) states via quantum purification method. In the previous work, we have already investigated an information-theoretic correspondence between the Gaussian maximally mixed states (GMMSs) and their purifications known as Gaussian maximally entangled states (GMESs) in [Phys. Lett. A {\bf 380}, 3607 (2016)]. We here compare an $N\times N$-dimensional maximally entangled state to the GMES we proposed previously, through an explicit calculation of quantum fidelity between those entangled states. By exploiting the results, we naturally conclude that our GMES is more suitable to the concept of \emph{maximally entangled} state in Gaussian quantum information, and thus it might be useful or applicable for quantum information tasks than the two-mode squeezed vacuum (TMSV) state in the Gaussian regime.