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Register a new userGeneral Hardy-Type Paradox Based on Bell inequality and its Experimental Test
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Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bells theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardys paradox is an important all-versus-nothing proof and is considered as the simplest form of Bells theorem. In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardys paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit two-setting case, and the corresponding successful probability is about four times larger than the original one, thus providing a more friendly test for experiment. We also find that GHZ paradox can be viewed as a perfect Hardy-type paradox. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.
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We report on a complete free-space field implementation of a modified Ekert91 protocol for quantum key distribution using entangled photon pairs. For each photon pair we perform a random choice between key generation and a Bell inequality. The amount of violation is used to determine the possible knowledge of an eavesdropper to ensure security of the distributed final key.
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 established a physically utilizable Bell inequality based on the Peres-Horodecki criterion. The new quadratic probabilistic Bell inequality naturally provides us a necessary and sufficient way to test all entangled two-qubit or qubit-qutrit states including the Werner states and the maximally entangled mixed states.
A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=infty$, at which $g_p$ is Euclidean. Broader implications are discussed.
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.
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