Simulability of high-dimensional quantum measurements

Abstract

We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an arbitrary quantum state $\rho$ are recovered exactly by first compressing $\rho$ into a lower dimensional space, followed by some quantum measurements. A full quantum compression is possible, i.e., leaving only classical information, if and only if the set $\mathcal{M}$ is jointly measurable. Our notion of simulability can thus be seen as a quantification of measurement incompatibility in terms of dimension. After defining these concepts, we provide an illustrative examples involving mutually unbiased basis, and develop a method based on semi-definite programming for constructing simulation models. In turn we analytically construct optimal simulation models for all projective measurements subjected to white noise or losses. Finally, we discuss how our approach connects with other concepts introduced in the context of quantum channels and quantum correlations.

References in corpus (6)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Joint measurability of generalized measurements implies classicality
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Operational relevance of resource theories of quantum measurements
• Incompatibility of quantum channels
• Implementation of quantum measurements using classical resources and only a single ancillary qubit

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• Joint-measurability and quantum communication with untrusted devices
• Shadow Simulation of Quantum Processes
• Naimark dilations of qubit POVMs and joint measurements
• Absolute dimensionality of quantum ensembles
• Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
• Compatibility of projective measurements subject to white noise and loss
• Compressing continuous variable quantum measurements
• Barycentric decomposition for quantum instruments
• On the simulation of quantum multimeters