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

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.

Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

“…One of the most important application is the oneside device-independent quantum key distribution: Suppose A can steer B by sharing a pair of entangled state, then by using only local measurements and classical communications, B can convince that the sharing quantum state is entangled through the communication between A and B. [16,20] Gaussian state is an important quantum states for continuous variable system which shows various applications, such as quantum communication and quantum-limited techniques for sensing, detection, and imaging. [18,19] Recent studies pointed out that the non-steerable states can be demonstrated to be useless for one-sided device-independent quantum key distribution.…”

“…[17] The effective steering relies DOI: 10.1002/andp.201700328 on the entanglement of quantum state, however, not all entangled quantum states have steering. [20][21][22][23][24][25][26] Gaussian steering is the quantum steering for Gaussian states under Gaussian measurement. [16,20] Gaussian state is an important quantum states for continuous variable system which shows various applications, such as quantum communication and quantum-limited techniques for sensing, detection, and imaging.…”

“…[18,19] Recent studies pointed out that the non-steerable states can be demonstrated to be useless for one-sided device-independent quantum key distribution. [16,20] Gaussian state is an important quantum states for continuous variable system which shows various applications, such as quantum communication and quantum-limited techniques for sensing, detection, and imaging. Especially, the atomic or solid state-based encoding of continuous variable systems provide a novel method that can be used for quantum information processing.…”

“…Moreover, the characterization of quantum correlations in Gaussian state is an important research branch and it attracts much attention recently. [20][21][22][23][24][25][26] Gaussian steering is the quantum steering for Gaussian states under Gaussian measurement. Wiseman et al [27,28] have first given the definition of Gaussian steering.…”

Monogamy relation in multipartite continuous-variable quantum teleportation

“…A strict monogamy relation was later found such that if one party has quantum correlation with a certain number parties, (s)he cannot be correlated with the other parties. Such a relation is proved to be true in quantum nonlocality [27] and quantum steering [28], particularly for Gaussian states under Gaussian measurement [29]. However, extended to non-Gaussian measurements, such a strict monogamy may break down even for Gaussian states [30].…”