Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages

Abstract

Einstein-Podolsky-Rosen (EPR) steering is often (implicitly or explicitly) taken to be evidence for spooky action-at-a-distance. An alternative perspective on steering is that Alice has no causal influence on the physical state of Bob's system; rather, Alice merely updates her knowledge of the state of Bob's system by performing a measurement on a system correlated with his. In this work, we elaborate on this perspective (from which the very term 'steering' is seen to be inappropriate), and we are led to a resource-theoretic treatment of correlations in EPR scenarios. For both bipartite and multipartite scenarios, we develop the resulting resource theory, wherein the free operations are local operations and shared randomness (LOSR). We show that resource conversion under free operations in this paradigm can be evaluated with a single instance of a semidefinite program, making the problem numerically tractable. Moreover, we find that the structure of the pre-order of resources features interesting properties, such as infinite families of incomparable resources. In showing this, we derive new EPR resource monotones. We also discuss advantages of our approach over a pre-existing proposal for a resource theory of 'steering', and discuss how our approach sheds light on basic questions, such as which multipartite assemblages are classically explainable.

arXiv commentV2 changes: Accepted by Quantum, bibliography hyperlinks adjusted according to journal policy. New narrative in the introduction

References in corpus (57)

• Quantum entanglement
• Concentrating Partial Entanglement by Local Operations
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Quantum Resource Theories
• Conditions for a class of entanglement transformations
• Operational Resource Theory of Coherence
• Fundamental limitations for quantum and nano thermodynamics
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Non-local correlations as an information theoretic resource
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Quantum Steering
• Theoretical framework for quantum networks
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Quantum Theory From Five Reasonable Axioms
• Quantum steering: a review with focus on semidefinite programming
• Work extraction and thermodynamics for individual quantum systems
• Quantum Mechanics as Quantum Information (and only a little more)
• The resource theory of informational nonequilibrium in thermodynamics
• Quantifying Einstein-Podolsky-Rosen steering
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
• Randomness vs Non Locality and Entanglement
• A mathematical theory of resources
• Towards a Formulation of Quantum Theory as a Causally Neutral Theory of Bayesian Inference
• Quantum speed limits, coherence and asymmetry
• All Entangled Quantum States Are Nonlocal
• Quantum marginal problem and N-representability
• Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
• Negativity and steering: a stronger Peres conjecture
• The resource theory of steering
• Unified criteria for multipartite quantum nonlocality
• Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
• Non-locality distillation and post-quantum theories with trivial communication complexity
• On nonlocality as a resource theory and nonlocality measures
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Scalable Bell inequalities for qubit graph states and robust self-testing
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
• Self-testing through EPR-steering
• The type-independent resource theory of local operations and shared randomness
• Type-independent Characterization of Spacelike Separated Resources
• Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective
• Nonlocality free wirings and the distinguishability between Bell boxes
• A channel-based framework for steering, non-locality and beyond
• Channel Steering
• Experimental multipartite entanglement and randomness certification of the W state in the quantum steering scenario
• Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
• Unscrambling the omelette of causation and inference: The framework of causal-inferential theories
• Necessary conditions on entanglement catalysts
• Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Bipartite post-quantum steering in generalised scenarios
• Quantifying athermality and quantum induced deviations from classical fluctuation relations
• Exposure of subtle multipartite quantum nonlocality

Cited by in corpus (12)

• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• The resource theory of nonclassicality of channel assemblages
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Every non-signalling channel is common-cause realizable
• Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing
• Activation of post-quantumness in bipartite generalised EPR scenarios
• Certifying nonlocal properties of noisy quantum operations
• Quantum Assemblage Tomography
• Operational Coherent Measurements with Steering and Randomness
• Localization of joint quantum measurements on ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ by entangled resources with Schmidt number at most $d$
• No-local-broadcasting theorem for non-signalling behaviours and assemblages
• Activation of post-quantum steering