Amplification uncertainty relation for probabilistic amplifiers

TL;DR

This paper derives a fundamental uncertainty-product limit for probabilistic quantum amplifiers using Gaussian states, revealing trade-offs in amplification noise and implications for entanglement distillation.

Contribution

It introduces an uncertainty-product amplification limit for general quantum operations based on canonical uncertainty relations, applicable to probabilistic amplifiers and entanglement distillation.

Findings

Derives a fundamental limit on amplification noise for probabilistic quantum channels.

Establishes a benchmark for non-Gaussian operations in quantum amplification.

Links amplification limits to entanglement distillation and local filtering.

Abstract

Traditionally, quantum amplification limit refers to the property of inevitable noise addition on canonical variables when the field amplitude of an unknown state is linearly transformed through a quantum channel. Recent theoretical studies have determined amplification limits for cases of probabilistic quantum channels or general quantum operations by specifying a set of input states or a state ensemble. However, it remains open how much excess noise on canonical variables is unavoidable and whether there exists a fundamental trade-off relation between the canonical pair in a general amplification process. In this paper we present an uncertainty-product form of amplification limits for general quantum operations by assuming an input ensemble of Gaussian distributed coherent states. It can be derived as a straightforward consequence of canonical uncertainty relations and retrieves basic properties of the traditional amplification limit. In addition, our amplification limit turns out to give a physical limitation on probabilistic reduction of an Einstein-Podolsky-Rosen uncertainty. In this regard, we find a condition that probabilistic amplifiers can be regarded as local filtering operations to distill entanglement. This condition establishes a clear benchmark to verify an advantage of non-Gaussian operations beyond Gaussian operations with a feasible input set of coherent states and standard homodyne measurements.