Measurement sharpness and disturbance tradeoff
arXiv:2308.04133 · doi:10.1103/PhysRevA.109.012201
Abstract
Obtaining information from a quantum system through a measurement typically disturbs its state. The postmeasurement states for a given measurement, however, are not unique and highly rely on the chosen measurement model, complicating the puzzle of information-disturbance. Two distinct questions are then in order. Firstly, what is the minimum disturbance a measurement may induce? Secondly, when a fixed disturbance occurs, how informative is the possible measurement in the best-case scenario? Here, we propose various approaches to tackle these questions and provide explicit solutions for the set of unbiased binary qubit measurements and postmeasurement state spaces that are equivalent to the image of a unital qubit channel. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces as well as the sharpness and quantum resources preserved in the postmeasurement states in terms of coherence and discord-like correlation once the measurement is applied locally.
arXiv comment10 pages, 2 figures
References in corpus (26)
- Quantifying Coherence
- Characterizing Nonclassical Correlations via Local Quantum Uncertainty
- Probabilistic theories with purification
- Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
- Coding Theorems for Quantum Channels
- An Invitation to Quantum Incompatibility
- Fidelity balance in quantum operations
- Balance between information gain and reversibility in weak measurement
- Global information balance in quantum measurements
- Experimental realization of a minimal disturbance quantum measurement
- Fidelity trade-off for finite ensembles of identically prepared qubits
- Information-disturbance tradeoff in quantum measurements
- Information-disturbance tradeoff in estimating a maximally entangled state
- Information-Disturbance Tradeoff in Quantum State Discrimination
- Uncertainty Relations for Positive Operator Valued Measures
- Strongly Incompatible Quantum Devices
- Qualitative Noise-Disturbance Relation for Quantum Measurements
- Unsharpness of generalized measurement and its effects in entropic uncertainty relations
- On the Sharpness and Bias of Quantum Effects
- Information, fidelity, and reversibility in general quantum measurements
- Quantumness of quantum channels
- Quasi inversion of qubit channels
- Complementarity Relation for Coherence and Disturbance
- Incompatibility of unbiased qubit observables and Pauli channels
- Quasi-inversion of quantum and classical channels in finite dimensions
- Quantifying unsharpness of observables in an outcome-independent way