Measurement by eraser

Postdoctoral fellow at the Institute for Quantum Computing (IQC) Aharon Brodutch and Eliahu Cohen (Tel Aviv University, University of Bristol) have developed a new method for designing complex quantum measurements.

Measurements are necessary for determining observable quantities – they tell us about the outcome of a quantum protocol and can also be part of a control sequence, such as an error detection and correction scheme. Brodutch and Cohen looked specifically at projective measurements – measurements that project the state of the system into a new state corresponding to the result. For example, when measuring spin, if the spin was ‘up’ and the resulting measurement is ‘up’, the spin remains ‘up’.

The researchers used the von Neumann measurement scheme and a quantum eraser to model a measurement that requires specific interactions between two physical systems that are challenging to construct. Brodutch and Cohen presented a protocol for carrying out non-local measurements – projective measurements of observable quantities on a system with parts at different locations. First, they performed simpler measurements that revealed too much information about the system and then erased parts of the results. The local measurement is erased, or undone, by making a conjugate, or incompatible, measurement and post-selecting the result.

For example, in a non-local parity measurement of a quantum system shared between two distant observers (shown in Figure 1), the observers want to know if their local states are correlated or anti-correlated with each other, without learning their specific values.

“These non-local measurements can protect entangled systems that have a similar property – they have a well-defined joint state, but undefined local states,” explained Brodutch. “Learning the local information is simple; each party can measure the state of their local system, but it destroys entanglement.”

The protocol Brodutch and Cohen present shows that it is possible to erase the unwanted local information while retaining the desired parity information, turning the local measurements into non-local ones.

The new protocol could be useful for other projective measurements on systems that cannot interact directly with each other, or in generating photon interactions or quantum gates for quantum computation. The results, Non-local Measurements via Quantum Erasure, appeared in Physical Review Letters February 18.