Relevance of rank for a mixed state quantum teleportation resource

TL;DR

This paper investigates how the rank of mixed entangled states influences their effectiveness as resources for quantum teleportation, revealing that higher rank states generally perform better and establishing bounds related to rank, fidelity, and concurrence.

Contribution

The study constructs new maximally entangled mixed states of different ranks and analyzes their teleportation capabilities, providing rank-dependent bounds and classifications.

Findings

Higher rank states are better for teleportation.

Low rank states require higher concurrence for fixed fidelity.

Existence of rank-dependent bounds on fidelity and concurrence.

Abstract

Mixed entangled states are generic resource for quantum teleportation. Optimal teleportation fidelity measures the success of quantum teleportation. The relevance of rank in the teleportation process is investigated by constructing three new maximally entangled mixed states (MEMS) of different ranks. Linear entropy, concurrence, optimal teleportation fidelity and Bell function are obtained for each of the state analytically. It is found that mixed states with higher rank are better resource for teleportation. In order to achieve a fixed value of optimal teleportation fidelity, we find that low rank states must have high concurrence. Further, for each of ranks 2, 3 and 4, we numerically generate 30000 maximally entangled mixed states. The analysis of these states reveals the existence of a rank dependent upper bound on optimal teleportation fidelity for a fixed purity. In order to achieve a fixed optimal teleportation fidelity, we find MEMS exhibit a rank dependent lower bound on concurrence. MEMS are classified in terms of their degree of nonlocality.