Measurement sharpness and disturbance tradeoff

TL;DR

This paper explores the fundamental tradeoff between measurement sharpness and disturbance in quantum systems, providing explicit solutions and tradeoff relations for qubit measurements and their effects on quantum resources.

Contribution

It introduces new approaches to quantify the measurement disturbance and sharpness tradeoff, with explicit solutions for unbiased binary qubit measurements and postmeasurement state spaces.

Findings

Different tradeoff relations between measurement sharpness and fidelity.

Explicit solutions for unbiased binary qubit measurements.

Tradeoffs involving quantum coherence and discord-like correlations.

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.