Abstract
The conflict between classical and quantum physics can be identified through a series of yes-no tests on quantum systems, without it being necessary that these systems be in special quantum states. Kochen-Specker (KS) sets of yes-no tests have this property and provide a quantum-versus-classical advantage that is free of the initialization problem that affects some quantum computers. Here, we report the first experimental implementation of a complete KS set that consists of 18 yes-no tests on four-dimensional quantum systems and show how to use the KS set to obtain a state-independent quantum advantage. We first demonstrate the unique power of this KS set for solving a task while avoiding the problem of state initialization. Such a demonstration is done by showing that, for 28 different quantum states encoded in the orbital-angular-momentum and polarization degrees of freedom of single photons, the KS set provides an impossible-to-beat solution. In a second experiment, we generate maximally contextual quantum correlations by performing compatible sequential measurements of the polarization and path of single photons. In this case, state independence is demonstrated for 15 different initial states. Maximum contextuality and state independence follow from the fact that the sequences of measurements project any initial quantum state onto one of the KS set's eigenstates. Our results show that KS sets can be used for quantum-information processing and quantum computation and pave the way for future developments.
Highlights
The classical description of nature is based on the assumption that all physical systems possess properties, such as position and velocity, that can be revealed by the act of observation and whose objective existence is independent of whether or not the observation does take place
The conflict between classical and quantum physics can be identified through a series of yes-no tests on quantum systems, without it being necessary that these systems be in special quantum states
The existence of KS sets demonstrates that, for any quantum state, it is impossible to reproduce the predictions of quantum mechanics (QM) with theories in which the measurement results are independent of other compatible measurements
Summary
The classical description of nature is based on the assumption that all physical systems possess properties, such as position and velocity, that can be revealed by the act of observation and whose objective existence is independent of whether or not the observation does take place. 3, there are sets of yes-no tests (represented in QM by projectors Åi 1⁄4 jviihvij onto unit vectors jvii) for which it is impossible to assign results 1 (yes) or 0 (no) in agreement with two predictions of QM. These sets, called KS sets, are universal in the sense that assigning results is impossible for any quantum state. The existence of KS sets demonstrates that, for any quantum state, it is impossible to reproduce the predictions of QM with theories in which the measurement results are independent of other compatible measurements. These theories are called noncontextual hidden variable (NCHV) theories.
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