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Register a new userExperimental detection of steerability in Bell local states with two measurement settings
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Steering, a quantum property stronger than entanglement but weaker than non-locality in the quantum correlation hierarchy, is a key resource for one-sided device-independent quantum key distribution applications, in which only one of the communicating parties is trusted. A fine-grained steering inequality was introduced in [PRA 90 050305(R) (2014)], enabling for the first time the detection of steering in all steerable two-qubit Werner states using only two measurement settings. Here we numerically and experimentally investigate this inequality for generalized Werner states and successfully detect steerability in a wide range of two-photon polarization-entangled Bell local states generated by a parametric down-conversion source.
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Entanglement is the defining feature of quantum mechanics, and understanding the phenomenon is essential at the foundational level and for future progress in quantum technology. The concept of steering was introduced in 1935 by Schrodinger as a generalization of the Einstein-Podolsky-Rosen (EPR) paradox. Surprisingly, it has only recently been formalized as a quantum information task with arbitrary bipartite states and measurements, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area have been restricted to the approach of Reid [PRA 40, 913], which followed the original EPR argument in considering only two different measurement settings per side. Here we implement more than two settings so as to be able to demonstrate experimentally, for the first time, that EPR-steering occurs for mixed entangled states that are Bell-local (that is, which cannot possibly demonstrate Bell-nonlocality). Unlike the case of Bell inequalities, increasing the number of measurement settings beyond two--we use up to six--dramatically increases the robustness of the EPR-steering phenomenon to noise.
We construct a simple algorithm to generate any CHSH type Bell inequality involving a party with two local binary measurements from two CHSH type inequalities without this party. The algorithm readily generalizes to situations, where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze new symmetric inequalities for four observers and three experimental settings per observer.
Bells theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bells inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this freedom of choice was addressed by ensuring that selection of measurement settings via conventional quantum random number generators was space-like separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bells inequality that, for the first time, uses distant astronomical sources as cosmic setting generators. In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photons color was set at emission, we observe statistically significant $gtrsim 7.31 sigma$ and $gtrsim 11.93 sigma$ violations of Bells inequality with estimated $p$-values of $ lesssim 1.8 times 10^{-13}$ and $lesssim 4.0 times 10^{-33}$, respectively, thereby pushing back by $sim$600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.
In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago, the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bells inequality by $9.3$ standard deviations, corresponding to an estimated $p$ value of $lesssim 7.4 times 10^{-21}$. This experiment pushes back to at least $sim 7.8$ Gyr ago the most recent time by which any local-realist influences could have exploited the freedom-of-choice loophole to engineer the observed Bell violation, excluding any such mechanism from $96%$ of the space-time volume of the past light cone of our experiment, extending from the big bang to today.
We give the complete list of 175 facet Bell inequalities for the case where Alice and Bob each choose their measurements from a set of four binary outcome measurements. For each inequality we compute the maximum quantum violation for qubits, the resistance to noise, and the minimal detection efficiency required for closing the detection loophole with maximally entangled qubit states, in the case where both detectors have the same efficiency (symmetric case).
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