Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Abstract

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

arXiv comment12 pages, 3 figures. Comments welcome! v4: published version in Quantum journal

References in corpus (37)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Bell nonlocality
• Device-independent security of quantum cryptography against collective attacks
• Significant-loophole-free test of Bell's theorem with entangled photons
• Random Numbers Certified by Bell's Theorem
• A strong loophole-free test of local realism
• No Signalling and Quantum Key Distribution
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• From Bell's Theorem to Secure Quantum Key Distribution
• Bounding the set of quantum correlations
• Probabilistic theories with purification
• Bell's inequalities and density matrices. Revealing hidden nonlocality.
• Free randomness can be amplified
• The Communication Cost of Simulating Bell Correlations
• Private Randomness Expansion With Untrusted Devices
• Randomness vs Non Locality and Entanglement
• Characterizing the nonlocal correlations of particles that never interacted
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Quantum causal modelling
• Beyond Bell's Theorem: Correlation Scenarios
• Almost quantum correlations
• Quantum common causes and quantum causal models
• How much measurement independence is needed in order to demonstrate nonlocality?
• Simple and tight device-independent security proofs
• Theory-independent limits on correlations from generalised Bayesian networks
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality
• On the Testability of Causal Models with Latent and Instrumental Variables
• Bounding the set of finite dimensional quantum correlations
• All reversible dynamics in maximally non-local theories are trivial
• Quantum violation of an instrumental test
• Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation
• Characterization of quantum correlations with local dimension constraints and its device-independent applications
• Margins of discrete Bayesian networks
• All CHSH polytopes
• Bell scenarios with communication
• Device-independent randomness generation with sublinear shared quantum resources

Cited by in corpus (23)

• Bell nonlocality in networks
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Quantum Inflation: A General Approach to Quantum Causal Compatibility
• Quantum speedup in the identification of cause-effect relations
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Single-photon nonlocality in quantum networks
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Quantifying causal influences in the presence of a quantum common cause
• Entanglement in prepare-and-measure scenarios: many questions, a few answers
• Experimental nonclassicality in a causal network without assuming freedom of choice
• Bipartite post-quantum steering in generalised scenarios
• Bell inequalities with one bit of communication
• Inflation: a Python library for classical and quantum causal compatibility
• A convergent inflation hierarchy for quantum causal structures
• Analysing causal structures in generalised probabilistic theories
• Quantum Causal Unravelling
• No nonlocal advantage of quantum coherence beyond quantum instrumentality
• Multistage games and Bell scenarios with communication
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Experimental test of quantum causal influences
• A minimal example of quantum non-classicality without freedom of choice
• A hierarchy of semidefinite programs for generalised Einstein-Podolsky-Rosen scenarios
• Fast tests for probing the causal structure of quantum processes