Optimal signal states for quantum detectors

Abstract

Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question of fundamental significance is how much information a quantum detector can extract from the quantum system it is applied to. In the present paper we address this question within a precise framework: given a quantum detector implementing a specific generalized quantum measurement, what is the optimal performance achievable with it for a concrete information readout task, and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks - the Bayes cost problem (of which minimal error discrimination is a special case), unambiguous message discrimination, and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information has an interpretation of a capacity of the measurement, and derive various properties that it satisfies, including its relation to the accessible information of an ensemble of states, and its form in the case of a group-covariant measurement. We illustrate our results with the example of a noisy two-level symmetric informationally complete measurement, for whose capacity we give analytical proofs of optimality. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.

13 pages, 1 figure, example section extended

References in corpus (12)

• Symmetric Informationally Complete Quantum Measurements
• General Entanglement Breaking Channels
• Unknown Quantum States: The Quantum de Finetti Representation
• Measuring measurement
• Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
• Coding Theorems for Quantum Channels
• Weak measurements are universal
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• Maximization of capacity and p-norms for some product channels
• Informational power of quantum measurements
• Optimal Unambiguous State Discrimination of two density matrices and its link with the Fidelity
• Distinguishability measures between ensembles of quantum states

Cited by in corpus (16)

• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• The SIC Question: History and State of Play
• Robustness of Measurement, discrimination games and accessible information
• Information capacity of quantum observable
• Informational power of the Hoggar SIC-POVM
• Linear Dependencies in Weyl-Heisenberg Orbits
• Maximally informative ensembles for SIC-POVMs in dimension 3
• Tight Bounds on the Accessible Information and the Informational Power
• Accessible Information and Informational Power of Quantum 2-designs
• Information capacity of continuous variable measurement channel
• On the classical capacity of quantum Gaussian measurement
• Hierarchy of Bounds on Accessible Information and Informational Power
• Communication capacity of mixed quantum t designs
• The information capacity of entanglement-assisted continuous variable measurement
• Discrimination power of a quantum detector
• Morphophoric POVMs, generalised qplexes, and 2-designs