Measurement incompatibility and quantum advantage in communication

Abstract

Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from d-dimensional classical systems assisted with shared randomness is the same as the set obtained from d-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks - a general version of random access codes - to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on d-dimensional systems, and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions - classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness - produced in communication scenarios.

18 pages

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Cited by in corpus (16)

• Compatibility of Generalized Noisy Qubit Measurements
• Unbounded quantum advantage in communication complexity measured by distinguishability
• Simple and general bounds on quantum random access codes
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Semi-device-independent certification of quantum non-Markovianity using sequential Random Access Codes
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Entanglement-breaking channels are a quantum memory resource
• Robust certification of quantum instruments through a sequential communication game
• Multi-object operational tasks for measurement incompatibility
• Relating CP divisibility of dynamical maps with compatibility of channels
• Semi-device-independent certification of number of measurements
• Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
• On compatibility of binary qubit measurements
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations
• Quantum advantage in a unified scenario and secure detection of resources
• Comparing quantum incompatibility of device sets from an operational perspective