Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states

TL;DR

This paper explores how the unique group structure of the Weyl-Heisenberg Bell basis influences the entanglement properties of Bell-diagonal states, revealing implications for quantum error correction and entanglement sharing.

Contribution

It demonstrates that the standard Bell basis's special structure leads to a higher share of PPT-entangled states and affects entanglement properties differently than other Bell bases.

Findings

Standard Bell basis has highest share of PPT and PPT-entangled states.

Group structure of Weyl-Heisenberg operators impacts error correction schemes.

Different Bell bases exhibit distinct entanglement structures.

Abstract

Maximally entangled Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl-Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies a equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of PPT-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.