We provide an interesting two-party parity-oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation noncontextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model: the usual local bound and a nontrivial preparation noncontextual bound arising from the nontrivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Alice and Bob perform three measurements of dichotomic observables in their respective sites. The optimal quantum value of the Bell expression in this scenario enables us to device-independently self-test the maximally entangled state and trine set of observables, three-outcome qubit positive-operator-valued measures and 1.58 bits of local randomness. Further, we generalize the above communication game in that both Alice and Bob perform the same but arbitrary (odd) number ($n>3$) of measurements. Based on the optimal quantum value of the relevant Bell expression for any arbitrary $n$, we also demonstrate device-independent self-testing of the state and measurements.
We provide an interesting two-party parity-oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation noncontextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model: the usual local bound and a nontrivial preparation noncontextual bound arising from the nontrivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Alice and Bob perform three measurements of dichotomic observables in their respective sites. The optimal quantum value of the Bell expression in this scenario enables us to device-independently self-test the maximally entangled state and trine set of observables, three-outcome qubit positive-operator-valued measures and 1.58 bits of local randomness. Further, we generalize the above communication game in that both Alice and Bob perform the same but arbitrary (odd) number (n>3) of measurements. Based on the optimal quantum value of the relevant Bell expression for any arbitrary n, we also demonstrate device-independent self-testing of the state and measurements.
A dimension witness provides a device-independent certification of the minimal dimension required to reproduce the observed data without imposing assumptions on the functioning of the devices used to generate the experimental statistics. In this paper, we provide a family of Bell expressions where Alice and Bob perform ${2}^{n\ensuremath{-}1}$ and n number of dichotomic measurements, respectively, which serve as the device-independent dimension witnesses of Hilbert space of 2m dimensions with $m=1,2,...,{2}^{\ensuremath{\lfloor}n/2\ensuremath{\rfloor}}$. The family of Bell expressions considered here determines the success probability of a communication game known as the n-bit parity-oblivious random access code. The parity obliviousness constraint is equivalent to the preparation noncontextuality assumption in an ontological model of an operational theory. For any given $n\ensuremath{\ge}3$, if such a constraint is imposed on the encoding scheme of the random access code, then the local bound of the Bell expression reduces to the preparation noncontextual bound. We provide explicit examples for the n=4and5 case to demonstrate that the relevant Bell expressions certify the qubit and two-qubit system, and for the n=6 case to demonstrate that the relevant Bell expression certifies the qubit, two-qubit, and three-qubit systems. We further demonstrate the sharing of quantum preparation contextuality by multiple Bobs sequentially to examine whether the number of Bobs sharing the preparation contextuality is dependent on the dimension of the system. We provide explicit examples of n=5 and 6 to demonstrate that the number of Bobs sequentially sharing the contextuality remains the same for any of the 2m-dimensional systems.
Abstract The parity-oblivious random-access-code (PORAC) is a class of communication games involving a sender (Alice) and a receiver (Bob). In such games, Alice’s amount of communication to Bob is constraint by the parity-oblivious (PO) conditions, so that the parity information of her inputs remains oblivious to Bob. The PO condition in an operational theory is equivalently represented in an ontological model that satisfies the preparation noncontextuality. In this paper, we provide a nontrivial generalization of the existing two-level PORAC and derive the winning probability of the game in the preparation noncontextual ontological model. We demonstrate that the quantum theory outperforms the preparation noncontextual model by predicting higher winning probability in our generalized PORAC.
We present a hitherto unexplored semi-device-independent (SDI) self-testing protocol designed to certify unitary operations within a variant of prepare-measure framework. We consider a communication game which we refer to as a variant of 3-bit prepare-measure random access code (PMRAC) involving two parties, Alice and Bob, who share a prior two-qubit quantum state. Alice encodes her message by applying unitary operations on her subsystem and sends it to Bob. To decode the message, Bob performs a measurement on the whole system. We demonstrate that the optimal quantum advantage of the variant of 3-bit PMRAC over the classical bound enables the self-testing of Alice's unitary operations and Bob's measurements. The derivation of the optimal quantum success probability is fully analytical. The approach is so elegant that it can be generalized for any arbitrary n-bit PMRAC and may also be extended to other prepare-measure communication games.
An ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.
Abstract We present a self-testing protocol in a constrained prepare-measure scenario, based on a communication game known as parity-oblivious multiplexing (POM) task. In this scenario, a parity-oblivious constraint is imposed on the preparations, allowing us to define a classical bound derived from a preparation noncontextual ontological model. We demonstrate that the optimal quantum value exceeds preparation noncontextual bound and therefore enables self-testing of the preparations and the measurement devices. Contrasting the prevailing consensus that the self-testing in prepare-measure scenario inevitably requires an upper bound on the dimension of the quantum system, we derive the optimal quantum success probability of the POM task devoid of assuming the dimension of the quantum system. Furthermore, by proving the existence of a unitary, we show that the optimal preparations and measurements in an unknown but finite dimensional Hilbert space, responsible for the observed input–output correlations, can be mapped, via a unitary, onto a known finite-dimensional quantum system. Our results thus pave the way for scalable, single system based certification protocols in the prepare-measure scenario.
Preparation contextuality is often manifested operationally through a quantitative advantage over preparation-noncontextual models in information-processing tasks, yet quantum theory typically falls short of perfect success. Here we introduce a parity-oblivious Hidden Matching task that instead yields an all-vs-nothing manifestation of preparation contextuality. Alice encodes an n-bit string so that her message reveals no information about any input parity other than the two-bit parities. Bob, given a perfect matching on the input positions, must output an edge of the matching together with the parity of its two bits. A quantum protocol using a single ⌈log2n⌉-qubit message satisfies the parity-obliviousness constraint and succeeds with certainty. We prove that no preparation-noncontextual model achieves perfect success for any even n≥6. The result holds for arbitrary ontic state spaces and assumes neither outcome determinism nor measurement noncontextuality. For n=6 and n=8, the optimal noncontextual success probabilities are 4/5 and 3/4, respectively, while asymptotically the optimal noncontextual success probability is 1/2+Θ(1/n). Our asymptotic upper bound follows from a Fourier-analytic sum rule derived via hypercontractivity on the Boolean hypercube. The resulting separation is qualitative rather than merely quantitative: quantum theory achieves perfect success, whereas preparation-noncontextual models cannot. We aslo show that at n=8 the noncontextual bound remains 3/4 even when Bob is restricted to just suitable 4 of the 105 possible perfect matchings, bringing the effect within experimental reach.