Role of fine-grained uncertainty in determining the limit of preparation contextuality

Abstract

The optimal success probability of a communication game sets fundamental limitations on an operational theory. Quantum advantage of parity oblivious random access code (PORAC), a communication game, over classical resources reveals the preparation contextuality of quantum theory [Phys. Rev. Lett. 102, 010401 (2009)]. Optimal quantum advantage in the N-dit PORAC game for finite dimensions is an open problem. Here, we show that the degree of uncertainty allowed in an operational theory determines the amount of preparation contextuality. We connect the upper bound of fine-grained uncertainty relation to the success probability of PORAC game played with the quantum resource. Subsequently, we find the optimal success probability for the 2-dit PORAC game using MUBs for the decoding strategy. Finally, we also derive an upper bound on quantum advantage for the N-dit PORAC game.

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References in corpus (20)

• Bell nonlocality
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Information Causality as a Physical Principle
• Entropic Uncertainty Relations and their Applications
• Contextuality for preparations, transformations, and unsharp measurements
• Quantum Steering
• A limit on nonlocality in any world in which communication complexity is not trivial
• Bloch vectors for qudits
• The uncertainty principle determines the non-locality of quantum mechanics
• Preparation contextuality powers parity-oblivious multiplexing
• Local Quantum Measurement and No-Signaling Imply Quantum Correlations
• Quantum Random Access Codes using Single $d$-level Systems
• Maximally epistemic interpretations of the quantum state and contextuality
• Optimal bounds for parity-oblivious random access codes
• Measurement incompatibility and steering are necessary and sufficient for operational contextuality
• Communication games reveal preparation contextuality
• Optimal quantum preparation contextuality in $n$-bit parity-oblivious multiplexing task
• Fine-grained uncertainty relations for several quantum measurements
• Ontological models, preparation contextuality and nonlocality
• Nonsignaling quantum random access code boxes

Cited by in corpus (4)

• Quantum Advantages in (n,d)->1 Random Access Codes
• Bloch sphere analog of qudits using Heisenberg-Weyl Operators
• Robust certification of quantum instruments through a sequential communication game
• Role of nonclassical temporal correlation in powering quantum random access codes