The unavoidable information flow to environment in quantum measurements

TL;DR

This paper demonstrates that in quantum measurements, information inevitably flows to the environment, requiring larger systems for subsequent measurements, and characterizes the conditions under which measurements can be sequentially implemented.

Contribution

It proves that sequential quantum measurements generally require access to a larger system, revealing the unavoidable information flow to the environment in quantum measurements.

Findings

Sequential measurements often need larger systems than the original input.

The class of measurements allowing any compatible subsequent measurement is characterized.

When the first observable is extreme, the classes of compatible and jointly measurable measurements coincide.

Abstract

One of the basic lessons of quantum theory is that one cannot obtain information on an unknown quantum state without disturbing it. Hence, by performing a certain measurement, we limit the other possible measurements that can be effectively implemented on the original input state. It has been recently shown that one can implement sequentially any device, either channel or observable, which is compatible with the first measurement [T. Heinosaari and T. Miyadera: Phys. Rev. A Vol 91 (2015), 022110]. In this work we prove that this can be done, apart from some special cases, only when the succeeding device is implemented on a larger system than just the input system. This means that some part of the still available quantum information has been flown to the environment and cannot be gathered by accessing the input system only. We characterize the size of the post-measurement system by determining the class of measurements for the observable in question that allow the subsequent realization of any measurement process compatible with the said observable. We also study the class of measurements that allow the subsequent realization of any observable jointly measurable with the first one and show that these two classes coincide when the first observable is extreme.