Unlimited One-Way Steering

Abstract

This work explores the asymmetry of quantum steering in a setup using high-dimensional entanglement. We construct entangled states with the following properties: $(i)$ one party (Alice) can never steer the state of the other party (Bob), considering the most general measurements, and $(ii)$ Bob can strongly steer the state of Alice, demonstrating genuine high-dimensional steering. In other words, Bob can convince Alice that they share an entangled state of arbitrarily high Schmidt number, while Alice can never convince Bob that the state is even simply entangled. In this sense, one-way steering can become unlimited. A key result for our construction is a condition for the joint measurability of all high-dimensional measurements subjected to the combined effect of noise and loss, which is of independent interest.

4+4 pages

References in corpus (33)

• Quantum entanglement
• Bell nonlocality
• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Quantum Steering
• Quantum steering: a review with focus on semidefinite programming
• Observation of one-way Einstein-Podolsky-Rosen steering
• Quantifying Einstein-Podolsky-Rosen steering
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• One-way Einstein-Podolsky-Rosen Steering
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Observation of genuine one-way Einstein-Podolsky-Rosen steering
• An Invitation to Quantum Incompatibility
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Joint measurability of generalized measurements implies classicality
• Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering
• One-to-one mapping between steering and joint measurability problems
• Asymmetric Gaussian steering: when Alice and Bob disagree
• Genuine hidden quantum nonlocality
• Sufficient criterion for guaranteeing that a two-qubit state is unsteerable
• Incompatible measurements in quantum information science
• Genuine high-dimensional quantum steering
• Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steering
• Asymmetric Gaussian harmonic steering in second harmonic generation
• Incompatibility breaking quantum channels
• Continuous variable steering and incompatibility via state-channel duality
• Quantifying Quantumness of Channels Without Entanglement
• Noise-Robust and Loss-Tolerant Quantum Steering with Qudits
• Simulability of high-dimensional quantum measurements
• Complete hierarchy for high-dimensional steering certification
• Robust genuine high-dimensional steering with many measurements
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Equivalence between simulability of high-dimensional measurements and high-dimensional steering

Cited by in corpus (8)

• Gaussian tripartite steering in Schwarzschild black hole
• Compatibility of Generalized Noisy Qubit Measurements
• The Schmidt rank for the commuting operator framework
• Can boundary configuration be tuned to optimize directional quantum steering harvesting?
• Analysis of Quantum Steering Measures
• Joint-measurability and quantum communication with untrusted devices
• Compatibility of projective measurements subject to white noise and loss
• Protection of quantum steering ellipsoids in non-Markovian environments