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Physical Review A

Certifying beyond quantumness of locally quantum no-signaling theories through a quantum-input Bell test

Edwin Peter Lobo, Sahil Gopalkrishna Naik, Samrat Sen, Ram Krishna Patra, Manik Banik, Mir Alimuddin

Published Oct 12, 2022• 10 citations
Publisher

Abstract

The authors study the correlations observed in quantum input Bell tests obtained from locally quantum no-signaling theories, which can reveal post-quantumness of bipartite ``beyond-quantum'' (i.e., more general than quantum) states that is undetectable with the standard classical input Bell tests. The study suggests the requirement of additional information principles to isolate the set of physical correlations.

DOI
10.1103/physreva.106.l040201

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The authors study the correlations observed in quantum input Bell tests obtained from locally quantum no-signaling theories, which can reveal post-quantumness of bipartite ``beyond-quantum'' (i.e., more general than quantum) states that is undetectable with the standard classical input Bell tests. The study suggests the requirement of additional information principles to isolate the set of physical correlations.
Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state can always be reproduced by quantum states and measurements, suggesting local quantum structure and no-signalling to be the axioms to isolate quantum correlations. In this letter, however, we show that if the Bell experiment is generalized to allow local quantum inputs, then beyond-quantum correlations can be generated by every beyond-quantum state. This gives us a way to certify beyond-quantumness of locally quantum no-signalling theories and in turn suggests requirement of additional information principles along with local quantum structure and no-signalling principle to isolate quantum correlations. More importantly, our work establishes that the additional principle(s) must be sensitive to the quantum signature of local inputs. We also generalize our results to multipartite locally quantum no-signalling theories and further analyze some interesting implications.
Physical theories with local structure similar to quantum theory can allow beyond-quantum global states that are in agreement with unentangled Gleason's theorem. In a standard Bell experiment any such bipartite state produces correlations that are always quantum simulable. In this limited classical-input-classical-output Bell scenario, we show that there exist bipartite beyond-quantum states that produce correlations all of which are in-fact classically simulable. However, if the type of Bell scenario is generalized to consider quantum states as inputs, we then show that any such bipartite beyond-quantum state yields beyond-quantum input-output correlations. We also analyze the implication of this quantum input scenario while studying generic multipartite correlations obtained from local quantum theory but potentially allowing different global structure. Our study suggests the requirement of type sensitive information principles for isolating the quantum correlations from the beyond-quantum ones.
No-signaling theories, which can contain nonlocal correlations stronger than quantum correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In practice, Bell tests are powerful tools to certify nonlocality, but their effectiveness is limited by the detector efficiency. In this work, we provide almost tight detection efficiency bounds for showing the nonlocality of no-signaling theories, by introducing a general class of Bell inequalities. In particular, we provide a tight bound for the bipartite case and an asymptotic tight bound for the multipartite case. The tightness of these bounds shows that they well characterize the structure of no-signaling theories. The bounds also imply that the detector efficiency requirement can be made arbitrarily low in both bipartite and multipartite cases by increasing the number of measurement settings. Furthermore, our work sheds light on the detector efficiency requirement for showing the nonlocality of the quantum theory.
Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
Characterising quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It has been shown that when considered with respect to so-called locally quantum observables, bipartite non-signalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) non-signalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalisation of no-signalling in the form of no-disturbance to dilated systems. We prove that non-signalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.
In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing k zero probabilities, we provide a (5−k) -parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set M of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of M in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.