Revealing universal quantum contextuality through communication games

Pan, A. K.

doi:10.1038/s41598-019-53701-5

Cited by 17 publications

(12 citation statements)

References 37 publications

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“…An ontological model of an operational quantum theory is considered to be preparation non-contextual if two preparation procedures P and P ′ prepare the same density matrix ρ, and no measurement can operationally distinguish the context by which ρ is prepared, i.e. ∀k, M : p(k|P, M) = p(k|P ′ , M) ⇒ ∀λ : µ(λ|ρ, P) = µ(λ|ρ, P ′ ), implying two ontic state distributions are equivalent irrespective of the contexts P and P ′ [71][72][73][74][75].…”

Section: Elegant Bell Inequality and Its Local And Preparation Non-co...mentioning

confidence: 99%

Device-independent self-testing of unsharp measurements

Roy

Pan

2023

New J. Phys.

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Semi-device-independent certification of an unsharp instrument has recently been demonstrated [New J. Phys. 21, 083034 (2019)] based on the sequential sharing of quantum advantages in a prepare-measure communication game by assuming the system to be qubit. In this work, we provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities where the devices are uncharacterized and the dimension of the system remains unspecified. We introduce an elegant sum-of-squares approach to derive the dimension-independent optimal quantum violation of Bell inequalities which plays a crucial role. Note that the standard Bell test cannot self-test the post-measurement states and consequently cannot self-test unsharp instruments. The sequential Bell test possesses the potential to self-test an unsharp instrument. We demonstrate that there exists a trade-off between the maximum sequential quantum violations of the Clauser-Horne-Shimony-Halt inequality, and they form an optimal pair that enables the DI self-testing of the entangled state, the observables, and the unsharpness parameter. Further, we extend our study to the case of elegant Bell inequality, and we argue that it has two classical bounds - the local bound and the non-trivial preparation non-contextual bound, lower than the local bound. Based on the sharing of preparation contextuality by three independent sequential observers, we demonstrate the DI self-testing of two unsharpness parameters. Since an experimental scenario involves losses and imperfection, we demonstrate the robustness of our certification to noise.

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Section: Elegant Bell Inequality and Its Local And Preparation Non-co...mentioning

confidence: 99%

Device-independent self-testing of unsharp measurements

Roy

Pan

2023

New J. Phys.

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“…An ontological model of an operational theory can be assumed to be non-contextual in the following way [4]; if two experimental procedures are equivalent in operational theory then they can be represented noncontextually in an ontological model. Then, an ontological model of quantum theory is assumed to be preparation non-contextual if ∀M, k : p(k|P, M ) = p(k|P , M ) ⇒ µ P (λ|ρ) = µ P (λ|ρ) (1) where the ρ is prepared by two distinct preparation procedures P and P [4,33,34]. We shall shortly see that in a preparation non-contextual ontological model the parity-oblivious constraint in a communication game in operational quantum theory implies equivalent obliviousness condition at the level of ontic states.…”

Section: A Operational Theory and Ontological Modelmentioning

confidence: 99%

Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

Pan

2021

Preprint

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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 non-contextuality 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 non-trivial preparation non-contextual bound arising from the non-trivial parityoblivious 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 deviceindependently self-test the maximally entangled state and trine-set of observables, three-outcome qubit positive-operator-valued-measures (POVMs) and 1.58 bit 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 have also demonstrated device-independent self-testing of state and measurements.

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“…The satisfaction of parityoblivious condition in an operational theory implies that no measurement can distinguish the parity of the inputs. This is regarded as an equivalent class of preparations [64,65,67] which will have equivalent representation at the level of the ontic states. It has been demonstrated in [62] that the parityobliviousness at the operational level must be satisfied at the level of ontic states if the ontological model of quantum theory is preparation non-contextual.…”

Section: Parity-oblivious Random-access-codementioning

confidence: 99%

“…Throughout this paper, by quantum advantage, we refer to the violation of preparation non-contextuality (unless stated otherwise) but to avoid clumsiness, we skip detailed discussion about it. We refer [62,64,65,67] for detailed discussion about it.…”

Section: Parity-oblivious Random-access-codementioning

confidence: 99%

Semi-device independent certification of multiple unsharpness parameters through sequential measurements

Mukherjee¹,

K.²

2021

Preprint

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Based on a sequential communication game, semi-device independent certification of an unsharp instrument has recently been demonstrated [New J. Phys. 21 083034 (2019), Phys. Rev. Research 2, 033014 (2020]. In this paper, we provide semi-device independent self-testing protocols in the prepare-measure scenario to certify multiple unsharpness parameters along with the states and the measurement settings. This is achieved through the sequential quantum advantage shared by multiple independent observers in a suitable communication game known as parity-oblivious random-access-code. We demonstrate that in 3-bit parity-oblivious random-accesscode, at most three independent observers can sequentially share quantum advantage. The optimal pair (triple) of quantum advantages enables us to uniquely certify the qubit states, the measurement settings, and the unsharpness parameter(s). The practical implementation of a given protocol involves inevitable losses. In a sub-optimal scenario, we derive a certified interval within which a specific unsharpness parameter has to be confined. We extend our treatment to the 4-bit case and show that at most two observers can share quantum advantage for the qubit system. Further, we provide a sketch to argue that four sequential observers can share the quantum advantage for the two-qubit system, thereby enabling the certification of three unsharpness parameters.

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Revealing universal quantum contextuality through communication games

Cited by 17 publications

References 37 publications

Device-independent self-testing of unsharp measurements

Device-independent self-testing of unsharp measurements

Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

Semi-device independent certification of multiple unsharpness parameters through sequential measurements

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