Observers can always generate nonlocal correlations without aligning measurements by covering all their bases

Abstract

Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal model, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party preforms measurements along three perpendicular directions on the Bloch sphere, then the parties will always violate a Bell inequality. Furthermore, we prove that this probability is highly robust against local depolarizing noise, in that small levels of noise only decrease the probability of violating a Bell inequality by a small amount. We also show that generalizing to N parties can increase the robustness against noise. These results improve on previous ones that only allowed a high probability of violating a Bell inequality for large numbers of parties. One of the most fascinating and useful features of quantum theory is that the correlations between the outcomes of spatially separated measurements can be nonlocal, i.e., inconsistent with any locally causal model [1,2]. Typically, to obtain nonlocal correlations experimentally, great care is taken to choose measurements that give the strongest nonlocal correlations possible, which requires distant parties to share a reference frame [3,4]. While there are proposals for violating a Bell inequality without the need for a prior shared reference frame [4,5], these proposals add substantial complexity to the simple form of a standard Bell test.Distant parties could attempt to violate a Bell inequality without aligning reference frames by performing measurements in random directions [6][7][8], and recent results prove that such a method can demonstrate a violation with some nonzero probability. Specifically, for N spatially-separated parties who share a GreenbergerHorne-Zeilinger (GHZ) state [9], almost all choices of two measurements at each site lead to nonlocal correlations between measurement outcomes if the number of parties N is large [7]. Therefore distant parties that do not share a reference frame can randomly choose measurements that violate some Bell inequality with a probability that approaches 1 as N increases. If the parties also share a single direction on the Bloch sphere (as can be the case in, e.g., photon polarization encodings [4]), then they can always violate one of two Bell inequalities by an amount that is exponential in N [8].These results are the weakest for the scenario most relevant to experiments, namely, the bipartite N = 2 case: the probability of violating a Bell inequality by choosing two mutually unbiased measurements randomly in the bipartite case is ∼ 42% [7]. In this paper, we show that if the two parties each choose three measurements corresponding to the x, y and z components of their local Cartesian reference frame (hereafter referred to as a triad of measuremen...

Detecting entanglement of unknown quantum states with random measurements

“…Given some prior knowledge of the density matrix (obtained, for example, by assuming that the given state is close to a target state that has been imperfectly prepared), few local measurements suffice to detect entanglement [2]. In a different vein, local measurements along randomly chosen directions may be used to certify nonclassical correlations by means of a Bell-inequality violation, if the state distributed between the different parties is known, thus obviating the need for a shared reference frame [3][4][5][6].…”

Complete experimental toolbox for alignment-free quantum communication

“…This is due to a filtering mechanism intrinsic to our universal-decoder set-up, which maps errors originating from beam rotations around axes other than the optical link, as well as other spatial perturbations, into signal losses instead of infidelity. Recently, interesting alignment-free approaches for QKD 43 and to extract non-local correlations [44][45][46] have been put forward. These, however, require that the relative axis orientations, though unknown, stay approximately static throughout the quantum data exchange session (see Supplementary Discussion for details).…”

Experimental bilocality violation without shared reference frames

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