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Here we present the most general framework for $n$-particle Hardys paradoxes, which include Hardys original one and Cerecedas extension as special cases. Remarkably, for any $nge 3$ we demonstrate that there always exist generalized paradoxes (with the success probability as high as $1/2^{n-1}$) that are stronger than the previous ones in showing the conflict of quantum mechanics with local realism. An experimental proposal to observe the stronger paradox is also presented for the case of three qubits. Furthermore, from these paradoxes we can construct the most general Hardys inequalities, which enable us to detect Bells nonlocality for more quantum states.
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Since the pillars of quantum theory were established, it was already noted that quantum physics may allow certain correlations defying any local realistic picture of nature, as first recognized by Einstein, Podolsky and Rosen. These quantum correlations, now termed quantum nonlocality and tested by violation of Bells inequality that consists of statistical correlations fulfilling local realism, have found loophole-free experimental confirmation. A more striking way to demonstrate the conflict exists, and can be extended to the multipartite scenario. Here we report experimental confirmation of such a striking way, the multipartite generalized Hardys paradoxes, in which no inequality is used and the conflict is stronger than that within just two parties. The paradoxes we are considering here belong to a general framework [S.-H. Jiang emph{et al.}, Phys. Rev. Lett. 120, 050403 (2018)], including previously known multipartite extensions of Hardys original paradox as special cases. The conflict shown here is stronger than in previous multipartite Hardys paradox. Thus, the demonstration of Hardy-typed quantum nonlocality becomes sharper than ever.
We establish a quantitative relation between Hardys paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the inconsistency of local realism with entanglement by Hardy is simplified if this breaking of measurement-disturbance relations is taken into account, and a much simplified experimental test of local realism is illustrated in the framework of Hardys thought experiment. The essence of Hardys model is identified as a combination of two conditional measurements, which give rise to definite eigenvalues to two non-commuting operators simultaneously in hidden-variables models. Better understanding of the intimate interplay of entanglement and measurement-disturbance is crucial in the current discussions of Hardys paradox using the idea of weak measurement, which is based on a general analysis of measurement-disturbance relations.
Tests such as Bells inequality and Hardys paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardys paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.
We test experimentally the quantum ``paradox proposed by Lucien Hardy in 1993 [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, namely its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically enforce non-contextuality, which must therefore be assumed based only on the observables compatibility. On the other hand, our single-particle experiment can be implemented more simply and allows larger detection efficiencies than typical two-particle ones, with a potential future advantage in terms of closing the detection loopholes.
A recent experimental proposal by Ahnert and Payne [S.E. Ahnert and M.C. Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak value predictions of Aharonov in Hardys paradox. This proposal contains flaws such as the state preparation method and the procedure for carrying out the requisite weak measurements. We identify previously published solutions to some of the flaws.
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