EPR Steering inequalities with Communication Assistance

Abstract

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with $c$ bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information ($c=1$), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.

arXiv comment14 pages, 3 figures. See also arXiv:1603.05079 for related work by A.B. Sainz et al

References in corpus (42)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Bell nonlocality
• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Experimental EPR-Steering of Bell-local States
• Observation of one-way Einstein-Podolsky-Rosen steering
• Quantifying Einstein-Podolsky-Rosen steering
• Distinguishing separable and entangled states
• The Communication Cost of Simulating Bell Correlations
• One-way Einstein-Podolsky-Rosen Steering
• Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
• Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering
• Genuine multipartite Einstein-Podolsky-Rosen steering
• Conclusive quantum steering with superconducting transition edge sensors
• Observation of genuine one-way Einstein-Podolsky-Rosen steering
• Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
• Grothendieck's constant and local models for noisy entangled quantum states
• Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering
• Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
• Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole
• Negativity and steering: a stronger Peres conjecture
• Quantum randomness extraction for various levels of characterization of the devices
• More efficient Bell inequalities for Werner states
• Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Local hidden--variable models for entangled quantum states
• General method for constructing local-hidden-variable models for entangled quantum states
• Algorithmic construction of local hidden variable models for entangled quantum states
• Bell Inequalities with Auxiliary Communication
• Unbounded violation of quantum steering inequalities
• Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
• Non-classicality thresholds for multiqubit states - numerical analysis
• Local hidden variable models for entangled quantum states using finite shared randomness
• Channel Steering
• Towards Grothendieck Constants and LHV Models in Quantum Mechanics
• The device-independent outlook on quantum physics (lecture notes on the power of Bell's theorem)
• Bell Inequalities with Communication Assistance

Cited by in corpus (11)

• Quantum steering: a review with focus on semidefinite programming
• Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
• Classical communication cost of quantum steering
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Quantum steering beyond instrumental causal networks
• Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
• Bounding the persistency of the nonlocality of W states
• Measurement-device-independent and arbitrarily loss-tolerant verification of quantum steering
• Measurement-device-independent verification of channel steering
• Beating one bit of communication with and without quantum pseudo-telepathy
• Demonstration that Einstein-Podolsky-Rosen steering requires more than one bit of faster-than-light information transmission