Entanglement-Breaking Indices

TL;DR

This paper introduces entanglement--breaking indices to quantify how many local channel iterations destroy entanglement, analyzing the effects of filtering operations and providing exact calculations for specific cases.

Contribution

It defines new entanglement--breaking indices, compares unitary and non-unitary filtering, and solves the depolarizing noise case for two-qubit systems.

Findings

Non-unitary filtering outperforms unitary filtering for dimensions ≥ 3.

No gap observed between filtering types in the qubit case, suggesting unitary filtering may be optimal.

Exact solution provided for depolarizing noise on two-qubit systems.

Abstract

We study a set of new functionals (called entanglement--breaking indices) which characterize how many local iterations of a given (local) quantum channel are needed in order to completely destroy the entanglement between the system of interest over which the transformation is defined and an external ancilla. The possibility of contrasting the noisy effects introduced by the channel iterations via the action of intermediate ({\it filtering}) transformations is analyzed. We provide some examples in which our functionals can be exactly calculated. The differences between unitary and non-unitary filtering operations are analyzed showing that, at least for systems of dimension $d$ larger than or equal to 3, the non-unitary choice is preferable (the gap between the performances of the two cases being divergent in some cases). For $d=2$ (qubit case) on the contrary no evidences of the presence of such gap is revealed: we conjecture that for this special case unitary filtering transformations are optimal. The scenario in which more general filtering protocols are allowed is also discussed in some detail. The case of a depolarizing noise acting on a two--qubit system is exactly solved in a general case.