The entangling power of non-entangling channels

TL;DR

This paper investigates the entangling power of non-entangling quantum channels, revealing conditions under which they can probabilistically increase entanglement and introducing a new Schmidt number for channels.

Contribution

It introduces the concept of stochastically non-entangling maps and a Schmidt number for channels, linking non-entangling channels to witness-preserving dual maps and Bell-like inequalities.

Findings

Non-entangling operations can increase the Schmidt number if they can generate entanglement probabilistically.

Channels are non-entangling iff their dual maps are witness-preserving.

Bell-like inequalities can detect entanglement generation in quantum processes.

Abstract

There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a non-entangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some non-zero probability. This is in stark contrast to the case where the parties of a quantum network are only able to control their joint state by local operations and classical communication (LOCC). There, being able to apply operations probabilistically (stochastic LOCC) does not increase the Schmidt number. Our findings show that certain non-entangling operations become entangling when selecting on specific measurement outcomes. This naturally leads us to the class of stochastically non-entangling maps, being those that cannot generate entanglement even probabilistically. Intrigued by this finding, we devise a Schmidt number for quantum channels that quantifies whether a channel can generate entanglement probabilistically. Moreover, we show that a channel is non-entangling if and only if its dual map is witness-preserving -- it takes entanglement witnesses to witnesses. Based on this finding, we derive Bell-like inequalities whose violation signals that a process generates entanglement.