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Register a new userThe Hardys nonlocality argument
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Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bells famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bells inequality. The alternative proofs of Bells theorem without using Bells inequality are known as `nonlocality without inequality (NLWI) proofs. We, review one such proof, namely the Hardys proof which due to its simplicity and generality has been considered the best version of Bells theorem.
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Logical nonlocality is completely characterized by Hardys paradox in (2,2,l) and (2,k,2) scenarios. We consider a variety of consequences and applications of this fact. (i) Polynomial algorithms may be given for deciding logical nonlocality in these scenarios. (ii) Bell states are the only entangled two-qubit states which are not logically nonlocal under projective measurements. (iii) It is possible to witness Hardy nonlocality with certainty in a simple tripartite quantum system. (iv) Noncommutativity of observables is necessary and sufficient for enabling logical nonlocality.
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.
We present an experimental realisation of Hardys thought experiment [Phys. Rev. Lett. {bf 68}, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variable based theories. The contradiction relies on non-maximally entangled position states of two particles.
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.
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.
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