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arXiv:1807.08791 · Physical Review A

Stronger tests of the collapse-locality loophole in Bell experiments

Adrian Kent

Published Jan 7, 2020• 9 citations
arXivHTMLPDF

Abstract

Several versions of quantum theory assume some form of localized collapse. If measurement outcomes are indeed defined by localized collapses, then a loophole-free demonstration of Bell nonlocality needs to ensure spacelike separated collapses associated with the measurements of the entangled systems. This collapse-locality loophole remains largely untested, with one significant exception probing Diosi's and Penrose's gravitationally induced collapse hypotheses. I distinguish two versions of the loophole, and focus on the more strongly motivated version, in which local hidden variables may depend causally on collapse outcomes but may not independently depend on measurement settings. I describe here techniques that allow much stronger experimental tests. These apply to all the well-known types of collapse postulate, including gravitationally induced collapse, spontaneous localization models, and Wigner's consciousness-induced collapse.

DOI
10.1103/physreva.101.012102

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Several versions of quantum theory assume some form of localized collapse. If measurement outcomes are indeed defined by localized collapses, then a loophole-free demonstration of Bell nonlocality needs to ensure spacelike separated collapses associated with the measurements of the entangled systems. This collapse-locality loophole remains largely untested, with one significant exception probing Diosi's and Penrose's gravitationally induced collapse hypotheses. I distinguish two versions of the loophole, and focus on the more strongly motivated version, in which local hidden variables may depend causally on collapse outcomes but may not independently depend on measurement settings. I describe here techniques that allow much stronger experimental tests. These apply to all the well-known types of collapse postulate, including gravitationally induced collapse, spontaneous localization models, and Wigner's consciousness-induced collapse.
Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no nonlocal correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise definition of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it evident that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments---the collapse locality loophole---which exists because of the possible time lag between a particle entering a measurement device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\ensuremath{\approx}0.1$ light seconds.
Collapse-locality is an untested loophole in the violation of Bell's inequalities. The core of the argument is that the time value of photon detection is delayed by the time Tc required by the collapse of its quantum state. The value of Tc is given by the underlying theory of quantum collapse, and is mostly unknown. Depending on the value of Tc, detections in the performed Bell's experiments may have not been truly space-like separated events. This implies that the inequalities may have been violated as a consequence of (conspiratorial) information propagating at subluminal speed. We report an optical Bell experiment which closes the weaker ('essential') form of this loophole regardless the theory of quantum collapse. This is possible thanks to unique features of the setup. These features are: classical signals sent to the stations to define a time reference, and variable distance between the stations leaving all other parameters constant.
Loophole-free violations of Bell inequalities imply that at least one of the assumptions behind local hidden-variable theories must fail. Here, we show that, if only one fails, then it has to fail completely, therefore excluding models that partially constrain freedom of choice or allow for partial retrocausal influences, or allow partial instantaneous actions at a distance. Specifically, we show that (i) any hidden-variable theory with outcome independence (OI) and arbitrary joint relaxation of measurement independence (MI) and parameter independence (PI) can be experimentally excluded in a Bell-like experiment with many settings on high-dimensional entangled states, and (ii) any hidden-variable theory with MI, PI and arbitrary relaxation of OI can be excluded in a Bell-like experiment with many settings on qubit-qubit entangled states. Loophole-free violations of Bell inequalities imply that at least one of the assumptions formalising local hidden-variable theories must fail. Here, the authors show that, if only one is false, then it has to fail completely, therefore excluding models that allow partial instantaneous actions at a distance, partially constrain freedom of choice or allow for partial retrocausal influences.
It is well known that there is a freedom-of-choice loophole or superdeterminism loophole in Bell's theorem. Since no experiment can completely rule out the possibility of superdeterminism, it seems that a local hidden variable theory consistent with relativity can never be excluded. In this paper, we present a new analysis of local hidden variable theories. The key is to notice that a local hidden variable theory assumes the universality of the Schroedinger equation, and it permits that a measurement can be in principle undone in the sense that the wave function of the composite system after the measurement can be restored to the initial state. We propose a variant of the EPR-Bohm experiment with reset operactions that can undo measurements. We find that according to quantum mechanics, when Alice's measurement is undone after she obtained her result, the correlation between the results of Alice's and Bob's measurements depends on the time order of these measurements, which may be spacelike separated. Since a local hidden variable theory consistent with relativity requires that relativistically non-invariant relations such as the time order of spacelike separated events have no physical significance, this result means that a local hidden variable theory cannot explain the correlation and reproduce all predictions of quantum mechanics even when assuming superdeterminism. This closes the major superdeterminism loophole in Bell's theorem.
We propose an experiment to test Bell nonlocality, a genuine nonclassicality, for the gravitational field. Two masses with embedded entangled spins (e.g., two diamonds with their NV-centre spins entangled) are placed well outside each other's light cones, ensuring a locality-loophole-free scenario. The spins are then coupled to the motion of their respective masses to generate spatial superpositions. Finally, local measurements are performed only on the gravitational fields of the two masses. If gravity is quantum, then the two entangled masses would entangle their gravitational fields, leading to correlations certifying Bell nonlocality of gravity. Trapped and ground-state cooled nano-objects with micron-sized spatial superposition are sufficient for this test. This goes beyond the recent proposals to test nonclassicality of gravity by providing, for the first time in the literature, a minimal tool to (i) create Einstein-Podolsky-Rosen (EPR) state of gravitational curvatures, (ii) witness entangled gravitational curvatures, (iii) rule out any local-realist description of gravity, and (iv) achieve a loophole-free test of gravity's nonclassicality in a fully device-independent way.