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A Class of Distance-Based Incompatibility Measures for Quantum Measurements
We discuss a recently proposed class of incompatibility measures for quantum measurements, which is based on quantifying the effect of measurements of one observable on the statistics of the outcome of another. We summarize the properties of this class of measures, and present a tight upper bound for the incompatibility of any set of projective measurements in finite dimensions. We also discuss non-projective measurements, and give a non-trivial upper bound on the mutual incompatibility of a pair of Luders instruments. Using the example of incompatible observables that commute on a subspace, we elucidate how this class of measures goes beyond uncertainty relations in quantifying the mutual incompatibility of quantum measurements.
Keywords
Entropic Uncertainty Relation, Fidelity, Incompatibility, Maximal Disturbance.
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- Heisenberg, W., Uber den anschaulichen inhalt der quantentheoretischen kinematik und mechanik. Z. Phys., 1927, 43(3–4), 172– 198; Robertson, H. P., The uncertainty principle. Phys. Rev., 1929, 34(1), 163–164.
- Wehner, S. and Winter, A., Entropic uncertainty relations – a survey. New J. Phys., 2010, 12(2), 025009-1 to 22.
- Fuchs, C. A. and Sasaki, M., Squeezing quantum information through a classical channel: measuring the quantumness of a set of quantum states. Quant. Inf. Comput., 2003, 3(5), 377–404.
- Bandyopadhyay, S. and Mandayam, P., Operational measure of incompatibility of noncommuting observables. Phys. Rev. A, 2013, 87, 042120-1 to 6.
- Mandayam, P. and Srinivas, M. D., Measures of disturbance and incompatibility for quantum measurements. Phys. Rev. A, 2014, 89(6), 062112-1 to 9.
- Mathai, A. M. and Rathie, P. N., Basic Concepts in Information Theory and Statistics, Wiley Eastern, New Delhi, 1975.
- Nielsen, M. A. and Chuang, I. L., Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
- Mandayam, P. and Srinivas, M. D., Disturbance trade-off principle for quantum measurements. Phys. Rev. A, 2014, 90(6), 062128-1 to 8.
- Kundu, S., Wagh, K. and Mandayam, P., Quantifying incompatibility beyond entropic uncertainty; arxiv:quant-ph/1510.04093.
- Heinosaari, T. and Ziman, M., The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement, Cambridge University Press, Cambridge, 2012.
- Srinivas, M. D., Optimal entropic uncertainty relation for successive measurements in quantum information theory. Pramana, 2003, 60(6), 1137–1152.
- Watrous, J., Semidefinite programs for completely bounded norms. Theor. Comput., 2009, 5, 217–238.
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