Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture

TL;DR

This paper investigates quantum steering in multimode Gaussian states, establishing monogamy relations, confirming the Peres conjecture, and analyzing the effects of noise and non-Gaussian measurements on steerability.

Contribution

It reformulates Gaussian steering criteria using purities, proves a strong monogamy relation, and confirms that only negative partial-transpose states exhibit steerability under Gaussian measurements.

Findings

Strong monogamy relation limits steering to one party

Only negative partial-transpose states can be steered by Gaussian measurements

Non-Gaussian measurements do not extend steerability beyond Gaussian measurements

Abstract

It is a topic of fundamental and practical importance how a quantum correlated state can be reliably distributed through a noisy channel for quantum information processing. The concept of quantum steering recently defined in a rigorous manner is relevant to study it under certain circumstances and we here address quantum steerability of Gaussian states to this aim. In particular, we attempt to reformulate the criterion for Gaussian steering in terms of local and global purities and show that it is sufficient and necessary for the case of steering a 1-mode system by a $N$-mode system. It subsequently enables us to reinforce a strong monogamy relation under which only one party can steer a local system of 1-mode. Moreover, we show that only a negative partial-transpose state can manifest quantum steerability by Gaussian measurements in relation to the Peres conjecture. We also discuss our formulation for the case of distributing a two-mode squeezed state via one-way quantum channels making dissipation and amplification effects, respectively. Finally, we extend our approach to include non-Gaussian measurements, more precisely, all orders of higher-order squeezing measurements, and find that this broad set of non-Gaussian measurements is not useful to demonstrate steering for Gaussian states beyond Gaussian measurements.