Abstract
The ultimate limits of measurement precision are dictated by the laws of quantum mechanics. One of the most fascinating results is that joint or simultaneous measurements of noncommuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for determining what an “optimal” joint measurement is, with corresponding different trade-off relations for the measurements. It is generally a nontrivial task to devise or implement a strategy that minimizes the joint-measurement uncertainty. Here, we implement the simplest possible technique for an optimal four-outcome joint measurement and demonstrate a type of optimal measurement that has not been realized before in a photonic setting. We experimentally investigate a joint-measurement uncertainty relation that is more fundamental in the sense that it refers only to probabilities and is independent of values assigned to measurement outcomes. Using a heralded single-photon source, we demonstrate quantum-limited performance of the scheme on single quanta. Since quantum measurements underpin many concepts in quantum information science, this study is both of fundamental interest and relevant for emerging photonic quantum technologies.
Highlights
There are several types of uncertainty relations in quantum mechanics
If two noncommuting observables are each measured separately, “ sharply”, the product of their variances is bounded from below by uncertainty relations [1,2,3]
Aside from their fundamental interest, uncertainty relations are relevant for quantum technology, including for quantum state estimation and quantum metrology
Summary
There are several types of uncertainty relations in quantum mechanics. To start with, if two noncommuting observables are each measured separately, “ sharply” (each observable measured on an ensemble of identically prepared quantum systems), the product of their variances is bounded from below by uncertainty relations [1,2,3]. Measurements generally disturb a measured quantum state This leads to further limitations on how well two observables can be measured jointly on the same quantum system. Uncertainty relations apply to measurements of any non-commuting observables, such as position and momentum, and spin-1/2 (qubit) observables. Aside from their fundamental interest, uncertainty relations are relevant for quantum technology, including for quantum state estimation and quantum metrology. They limit how much we can learn about different properties of quantum systems, and are related to why one can bound the information held by an eavesdropper in quantum key distribution
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