Hilbert-Schmidt disturbance due to measurement

Michael R. Frey

doi:10.1117/12.777143

27 March 2008 Hilbert-Schmidt disturbance due to measurement

Michael R. Frey

Proceedings Volume 6976, Quantum Information and Computation VI; 69760D (2008) https://doi.org/10.1117/12.777143
Event: SPIE Defense and Security Symposium, 2008, Orlando, Florida, United States

Abstract

We define quantum state disturbance in terms of Hilbert-Schmidt (HS) distance, finding according to this definition that measurements and unitary operations drive qubit states along straight lines and circles, respectively, in HS geometry. We establish conditions for additive disturbance; the straigh-line signature of quantum measurement is a direct consequence of this additivity. Also, state disturbance defined by HS distance is contrapuntally related to information gain measured by state discrimination probability. We use these quantifiers of state disturbance and information gain to elaborate the trade-off between the two. Explicitly identified in this trade-off between information gain and state disturbance is the mechanism-the measurement strength-that mediates the trade-off.

Citation Download Citation

Michael R. Frey "Hilbert-Schmidt disturbance due to measurement", Proc. SPIE 6976, Quantum Information and Computation VI, 69760D (27 March 2008); https://doi.org/10.1117/12.777143

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