Amortization does not enhance the max-Rains information of a quantum channel

TL;DR

This paper proves that amortization does not increase the max-Rains entanglement measure of quantum channels, providing a new upper bound on their PPT-P assisted quantum capacity with implications for quantum communication.

Contribution

It demonstrates that amortized entanglement does not enhance max-Rains information, offering a single-letter bound on PPT-P assisted quantum capacity using SDP techniques.

Findings

Amortization does not increase max-Rains entanglement.

Provides a computable upper bound on PPT-P assisted quantum capacity.

Establishes a benchmark for LOCC-assisted quantum capacity.

Abstract

Given an entanglement measure $E$, the entanglement of a quantum channel is defined as the largest amount of entanglement $E$ that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement $E$ that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and a channel's max-Rains information, found recently in [Wang et al., arXiv:1709.00200]. The main application of our result is a single-letter, strong-converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.