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Physical Review Letters

How to ascertain the values of sigmax , σy , and σz of a spin-1/2particle

Lev Vaidman A, Yakir Aharonov, David Z. Albert

Published Apr 6, 1987• 128 citations
Publisher

Abstract

A procedure is described whereby the result of the measurement of any of the three Cartesian components of the spin of a single spin-(1/2) particle at a single time can be inferred with certainty from the result of two other measurements, one of which is carried out before, and the other after, the time in question.
DOI
10.1103/physrevlett.58.1385

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Experimental Investigations of Uncertainty Relations Inherent in Successive $$1/2-$$Spin Measurements

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We discuss two questions related to the concept of weak values as seen from the standard quantum-mechanics point of view. In the first part of the paper, we describe a scenario where unphysical results similar to those encountered in the study of weak values are obtained using a simple experimental setup that does not involve weak measurements. In the second part of the paper, we discuss the correct physical description, according to quantum mechanics, of what is being measured in a weak-value-type experiment.
In the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of sigma(x), sigma(y), and sigma(z) of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.
We show that dynamics in the spin–orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a particle by comparing two examples of such a procedure. The first example is a simultaneous measurement of spin components, σ x and σ y , corresponding to non-commuting operators, which cannot be accurately obtained together at a given time instant due to the Heisenberg uncertainty ratio. By mapping spin dynamics onto a spatial walk, such a procedure determines measurement-time averages of σ x and σ y , which can already be precisely evaluated in a single short-time measurement. The other, qualitatively different, example is the spin of a one-dimensional particle in a magnetic field. Here, the measurement outcome depends on the angle between the spin–orbit coupling and magnetic fields. These results can be applied to studies of spin–orbit coupled cold atoms and electrons in solids.
Experimental Investigations of Uncertainty Relations Inherent in Successive 1/2−1/2-1/2−Spin Measurements