A simple formula for pooling knowledge about a quantum system

Abstract

When various observers obtain information in an independent fashion about a classical system, there is a simple rule which allows them to pool their knowledge, and this requires only the states-of-knowledge of the respective observers. Here we derive an equivalent quantum formula. While its realm of applicability is necessarily more limited, it does apply to a large class of measurements, and we show explicitly for a single qubit that it satisfies the intuitive notions of what it means to pool knowledge about a quantum system. This analysis also provides a physical interpretation for the trace of the product of two density matrices.

5 pages, Revtex4

References in corpus (2)

• Information-disturbance tradeoff in quantum measurement on the uniform ensemble and on the mutually unbiased bases
• Stochastic simulations of conditional states of partially observed systems, quantum and classical

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• Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
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• Pooling quantum states obtained by indirect measurements
• Compatibility of state assignments and pooling of information
• Symmetry and Topology of Successive Quantum Feedback Control