Approximate virtual quantum broadcasting

TL;DR

This paper introduces a method for approximate virtual quantum broadcasting that reduces sample size requirements by allowing small systematic bias, overcoming limitations of previous no-broadcasting approaches.

Contribution

It develops efficient semidefinite programs to determine minimal sample sizes for approximate virtual quantum broadcasting with controlled error.

Findings

Approximate virtual broadcasting is feasible with smaller samples than naive methods.

Symmetry-based simplifications enable characterization via depolarizing channels.

The approach balances bias and sample size to optimize quantum information distribution.

Abstract

The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.