Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses

Abstract

We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by $d$-dimensional states, and that rely only upon a simple property of the set of measurements used (the maximal overlap between measurement directions). Using these inequalities we show that the critical detection efficiency above which $n$ von Neumann measurements can demonstrate steering is $1/n$. We show furthermore that using our construction and high dimensional states allows for steering demonstrations which are also highly robust to depolarising noise and produce unbounded violations in the presence of loss. Finally, our results provide an explicit means to certify the non-joint measurability of any set of inefficient von Neuman measurements.

4+3 pages. v2: title changed. Results on unbounded violation of steering inequalities added. Accepted by PRA

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Hacking commercial quantum cryptography systems by tailored bright illumination
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Joint measurability of generalized measurements implies classicality
• Noise robustness of the nonlocality of entangled quantum states
• Optimal Measurements for Tests of EPR-Steering with No Detection Loophole using Two-Qubit Werner States

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• Genuine high-dimensional quantum steering
• Quantifying measurement incompatibility of mutually unbiased bases
• Steering criteria from general entropic uncertainty relations
• Measurement incompatibility does not give rise to Bell violation in general
• Universal steering inequalities
• Incompatibility breaking quantum channels
• Retrieving High-Dimensional Quantum Steering From a Noisy Environment with N Measurement Settings
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Noise-Robust and Loss-Tolerant Quantum Steering with Qudits
• Quantum steering inequality with tolerance for measurement-setting-errors: experimentally feasible signature of unbounded violation
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• Quantum steering with imprecise measurements
• Certification of incompatible measurements using quantum steering
• Complete hierarchy for high-dimensional steering certification
• Incompatible measurements on quantum causal networks
• Scalable entanglement certification via quantum communication
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Semidefinite relaxations for high-dimensional entanglement in the steering scenario
• Distrustful quantum steering
• Measurement-device-independent and arbitrarily loss-tolerant verification of quantum steering
• The Schmidt rank for the commuting operator framework
• Adjusting inequalities for detection-loophole-free steering experiments
• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios
• Verification of joint measurability using phase-space quasiprobability distributions
• Joint-measurability and quantum communication with untrusted devices
• Maximal violation of steering inequalities and the matrix cube
• Measurement-device-independent verification of channel steering
• Violation of steering inequality for generalized equiangular measurements
• Steering nonlocality in high-speed telecommunication system without detection loophole
• Choice of mutually unbiased bases and outcome labelling affects measurement outcome secrecy
• Multipartite steering verification with imprecise measurements
• On compatibility of binary qubit measurements
• Witness High-Dimensional Quantum Steering via Majorization Lattice