Complete Information Balance in Quantum Measurement

TL;DR

This paper establishes a comprehensive set of trade-off relations among information gain, disturbance, and reversibility in quantum measurement, revealing an information conservation law crucial for quantum information processing.

Contribution

It introduces a complete framework for the information balance in quantum measurement, including reversibility, which was previously overlooked.

Findings

Derived all pairs of trade-off relations involving information gain, disturbance, and reversibility.

Identified conditions for optimal measurements satisfying the conservation laws.

Reversibility is shown to be essential for a complete information balance in quantum measurement.

Abstract

Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain, state disturbance and reversibility, together with their fundamental relations. Numerous efforts have been made to obtain the trade-off between information gain and state disturbance, which becomes a practical basis for secure information processing. However, a complete information balance is necessary to include the reversibility of quantum measurement, which constitutes an integral part of practical quantum information processing. We here establish all pairs of trade-off relations involving information gain, disturbance, and reversibility, and crucially the one among all of them together. By doing so, we show that the reversibility plays a vital role in completing the information balance. Remarkably, our result can be interpreted as an information-conservation law of quantum measurement in a nontrivial form. We completely identify the conditions for optimal measurements that satisfy the conservation for each tradeoff relation with their potential applications. Our work can provide a useful guideline for designing a quantum measurement in accordance with the aims of quantum information processors.