Experimentally feasible measures of distance between quantum operations

Abstract

We present two measures of distance between quantum processes based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. As the behavior of the superfidelity between quantum processes is crucial for the properties of the introduced measures, we study its behavior for several families of quantum channels. We calculate superfidelity between arbitrary one-qubit channels using affine parametrization and superfidelity between generalized Pauli channels in arbitrary dimensions. Statistical behavior of the proposed quantities for the ensembles of quantum operations in low dimensions indicates that the proposed measures can be indeed used to distinguish quantum processes.

9 pages, 4 figures

References in corpus (7)

• Quantum Process Tomography: Resource Analysis of Different Strategies
• Memory effects in quantum channel discrimination
• Unambiguous discrimination among quantum operations
• Alternative fidelity measure for quantum states
• Random Quantum Operations
• Continuity of quantum channel capacities
• Bound on trace distance based on superfidelity

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• Measuring the degree of unitarity for any quantum process