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arXiv:0709.2910 · Physics Letters A

Entanglement, weak values, and the precise inference of joint measurement outcomes for non-commuting observable pairs

Alonso Botero

Published Dec 10, 2009• 3 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2009.12.010

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Abstract In questioning the completeness of quantum mechanics, Einstein–Podolsky–Rosen (EPR) claimed that from the outcomes of local experiments performed on an entangled system, it was possible to ascribe simultaneous reality to the values of certain incompatible observables. As EPR acknowledged, the inevitable disturbance of quantum measurements prevents the precise verification of these assertions on a single system. However, the EPR elements of reality can still be tested at the ensemble level through weak measurements—which minimally disturb the measured system—by interpreting the EPR assertions as assertions about weak values that follow from the outcomes of projective measurements. Here, we report an implementation of such a test through joint weak measurements followed by post-selection on polarization-entangled photon pairs. Our results show that there is a correspondence between the obtained joint weak values and the inferred elements of reality in the polarization version of the EPR assertions.
Quantum mechanics does not permit joint measurements of non-commuting observables.However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property.The results can be interpreted as complex joint probabilities of the two non-commuting measurement outcomes.Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state.We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental state-independent relations between non-commuting properties that represent the most fundamental form of universal laws in quantum physics.