Unified picture for spatial, temporal and channel steering

Abstract

Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight steering inequalities for all three scenarios. Moreover, we show that certain notions of temporal and spatial steering are fully equivalent and prove a hierarchy between temporal steering and macrorealistic hidden variable models.

7 pages, 2 figures

References in corpus (12)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Joint measurability of generalized measurements implies classicality
• Grothendieck's constant and local models for noisy entangled quantum states
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
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• Adaptive strategy for joint measurements
• Channel Steering
• Joint Measurability and Temporal Steering
• Quantum correlations with a gap between the sequential and spatial cases

Cited by in corpus (17)

• Quantum Steering
• Incompatible measurements in quantum information science
• Steering criteria from general entropic uncertainty relations
• Set coherence: basis-independent quantification of quantum coherence
• Experimental test of non-macrorealistic cat-states in the cloud
• Quantifying Quantumness of Channels Without Entanglement
• Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems
• Hierarchy in temporal quantum correlations
• Leggett-Garg Macrorealism and temporal correlations
• Measurement incompatibility and quantum advantage in communication
• Quantum measurement incompatibility in subspaces
• Benchmarking Quantum State Transfer on Quantum Devices using Spatio-Temporal Steering
• Necessary and sufficient condition for joint measurability
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Semi-device-independently characterizing quantum temporal correlations
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations