How Quantum Correlations Enhance Prediction of Complementary Measurements

Abstract

If there are correlations between two qubits, then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question as to what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary knowledge excesses are used. A nontrivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.

Coherent versus incoherent sequential quantum measurements

“…Further, the complementary measurements on the qubit P can be predicted from the qubit S still with a quantum enhancement in the complementary correlations, according to Ref. [16]. Note that the feedforward cannot be applied to qubit P , since the preparation is considered to be completely independent and unaccessible from the measurement.…”

“…Since the nondestructive monitoring of alternatives in the duality experiment is directly reducing only off-diagonal elements in a preferred measurement basis, the visibility exactly reflects the decoherence process [14]. If the duality is discussed rather in a context of a Einstein-Podolsky-Rosen argument, the variances [15] and knowledge [16] are considered to be alternative measures of decoherence.…”

“…A more advanced form of entanglement has the maximal Bell factor B max [20,21] over two, which is a witness of the quantum correlations without any local hidden variable model. Quantitatively, B max gives an upper bound on predictions of the complementary measurements enhanced by the quantum correlations [16].…”

Testing sequential quantum measurements: how can maximal knowledge be extracted?

“…Future steps might be the study of the extension for multiple measurements and the application to continuos measurements for controlled dynamics and others quantum information protocols3637. Here we considered sequential measurements of compatible observables, future work will focus on different scenarios of complementary measurements38 and non-compatible observables.…”