Abstract
Contextuality is a phenomenon at the heart of the quantum mechanical departure from classical behaviour, and has been recently identified as a resource in quantum computation. Experimental demonstration of contextuality is thus an important goal. The traditional form of contextuality -- as violation of a Kochen-Specker inequality -- requires a quantum system with at least three levels, and the status of the assumption of determinism used in deriving those inequalities has been controversial. By considering `unsharp' observables, Liang, Spekkens and Wiseman (LSW) derived an inequality for generalized noncontextual models that doesn't assume determinism, and applies already to a qubit. We experimentally implement the LSW test using the polarization states of a heralded single photon and three unsharp binary measurements. We violate the LSW inequality by more than 16 standard deviations, thus showing that our results cannot be reproduced by a noncontextual subset of quantum theory.
Highlights
There are a number of proposals for tests which pit quantum mechanics against alternative views of reality, including the theorems of Bell [1] and of Kochen and Specker (KS) [2]
[22] that these works make an unwarranted assumption of determinism for unsharp measurements
The relevant class is the unsharp projective measurements, in which each of the set of orthogonal projectors is mixed in some ratio with other projectors from the same set, in order to make the positive operator-valued measures (POVMs). The LSW assumption is that the response function is likewise a mixture of the deterministic response functions assumed by KS for projective measurements, in the same ratios
Summary
There are a number of proposals for tests which pit quantum mechanics against alternative views of reality, including the theorems of Bell [1] and of Kochen and Specker (KS) [2]. The KS theorem has the advantage of applying to a single system, and states that noncontextual hidden variable theories are incompatible with quantum predictions, under the assumption that the measurements can be described by projectors. To find simpler proofs of contextuality, applicable to a qubit (two-level system), generalizations of KS noncontextuality have been proposed [18,19,20,21] These all utilise generalized measurements, described by positive operator-valued measures (POVMs). ( each element of the POVM commutes with each other element, just as for a projective measurement.) The LSW assumption is that the response function is likewise a mixture of the deterministic response functions assumed by KS for projective measurements, in the same ratios Using this principle, LSW derived a generalized noncontextuality inequality involving three different unsharp projective measurements on a qubit. There, the state preparations and measurements are realized with time-sharing methods, and the problem of noises in measurements is solved with a technique derived within the framework of generalised probabilistic theories
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