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Coexistence of quantum effects. (English) Zbl 1169.81304

Summary: The witness set \(\mathcal W(A, B)\) for two quantum effects A, B is the set of effects that verify the coexistence of \(A\) and \(B\). We first study the properties of \(\mathcal W(A, B)\). We then introduce a measure of sharpness \(\mathcal S_{n}(A)\) for an \(n\)-dimensional quantum effect \(A\). We show that \(\mathcal S_{2}(A)\) has natural properties that a measure of sharpness should possess and conjecture that \(\mathcal S_{n}(A)\) also has these properties for \(n > 2\). Finally, we employ \(\mathcal S_{2}(A)\) to obtain a characterization for the coexistence of two qubit effects in terms of operational parameters.

MSC:

81P05 General and philosophical questions in quantum theory
81P15 Quantum measurement theory, state operations, state preparations
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References:

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