Contextuality sans incompatibility in the simplest scenario: Communication supremacy of a qubit
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arXiv
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| Natura: | Preprint |
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2025
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| author | Patra, Partha Mukherjee, Sumit Pan, A. K. |
| author_facet | Patra, Partha Mukherjee, Sumit Pan, A. K. |
| contents | Conventional wisdom asserts that measurement incompatibility is necessary for revealing the non-locality and contextuality. In contrast, a recent work [Phys. Rev. Lett. 130, 230201 (2023)] demonstrates the generalized contextuality without measurement incompatibility by using a five-outcome qubit measurement. In this paper, we introduce a two-party prepare-measure communication game involving specific constraints on preparations, and we demonstrate contextuality sans incompatibility in the simplest measurement scenario, requiring only a three-outcome extremal qubit measurement. This contrasts with the aforementioned five-outcome qubit measurement, which can be simulated by an appropriate convex mixture of five three-outcome incompatible qubit measurements. Furthermore, we illustrate that our result has a prominent implication in information theory. Our communication game can be perceived as a constrained Holevo-Frankle-Weiner (HFW) scenario, as operational restrictions are imposed on preparations. We show that the maximum success probability of the game by using a qubit surpasses that attainable by a c-bit, even when shared randomness is a free resource. Consequently, this finding exemplifies the supremacy of a qubit over a c-bit within a constrained HFW framework. Thus, alongside offering fresh insights into quantum foundations, our results pave a novel pathway for exploring the efficacy of a qubit in information processing tasks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contextuality sans incompatibility in the simplest scenario: Communication supremacy of a qubit Patra, Partha Mukherjee, Sumit Pan, A. K. Quantum Physics Conventional wisdom asserts that measurement incompatibility is necessary for revealing the non-locality and contextuality. In contrast, a recent work [Phys. Rev. Lett. 130, 230201 (2023)] demonstrates the generalized contextuality without measurement incompatibility by using a five-outcome qubit measurement. In this paper, we introduce a two-party prepare-measure communication game involving specific constraints on preparations, and we demonstrate contextuality sans incompatibility in the simplest measurement scenario, requiring only a three-outcome extremal qubit measurement. This contrasts with the aforementioned five-outcome qubit measurement, which can be simulated by an appropriate convex mixture of five three-outcome incompatible qubit measurements. Furthermore, we illustrate that our result has a prominent implication in information theory. Our communication game can be perceived as a constrained Holevo-Frankle-Weiner (HFW) scenario, as operational restrictions are imposed on preparations. We show that the maximum success probability of the game by using a qubit surpasses that attainable by a c-bit, even when shared randomness is a free resource. Consequently, this finding exemplifies the supremacy of a qubit over a c-bit within a constrained HFW framework. Thus, alongside offering fresh insights into quantum foundations, our results pave a novel pathway for exploring the efficacy of a qubit in information processing tasks. |
| title | Contextuality sans incompatibility in the simplest scenario: Communication supremacy of a qubit |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.09534 |