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arXiv:2106.07945 · Physical Review A

Simulations of quantum nonlocality with local negative bits

Kelvin Onggadinata, Paweł Kurzyński, Dagomir Kaszlikowski

Published Sep 6, 2023• 5 citations
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Abstract

We propose a simple simulation of nonlocal quantum correlations among $N$ qubits using a local hidden variable source with a positive probability distribution, given that each of the $N$ observers has access to a local negative bit. Notably, unlike the Toner-Bacon protocol, no exchange of classical bits between the observers is required. Moreover, our simulation can be extended to include Popescu-Rohrlich box correlations.

DOI
10.1103/physreva.108.032204

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We propose a simple simulation of nonlocal quantum correlations among NNN qubits using a local hidden variable source with a positive probability distribution, given that each of the NNN observers has access to a local negative bit. Notably, unlike the Toner-Bacon protocol, no exchange of classical bits between the observers is required. Moreover, our simulation can be extended to include Popescu-Rohrlich box correlations.
Bell nonlocality exemplifies the most profound departure of quantum theory from classical realism. Yet, the extent of nonlocality in quantum theory is intrinsically bounded, falling short of the correlations permitted by the relativistic causality (the no-signaling) principle. A paradigmatic example is the Popescu-Rohrlich correlation: two distant parties sharing arbitrary entanglement cannot achieve this correlation, though it can be simulated with classical communication between them. Here we show how such post-quantum correlations can instead be simulated using intrinsically non-signaling physical resources, and implement the proposed scheme using a quantum circuit on a four-qubit photonic platform. Unlike the conventional approaches, our method exploits dynamical correlations between distinct physical systems, with intrinsic randomness suppressing any signaling capacity. This enables the realization of post-quantum correlations both with and without entanglement. We also analyze how the simulation scheme extends to beyond quantum nonlocal correlations in multipartite systems. Our experimental demonstration using a photonic system establishes a versatile framework for exploring post-quantum correlations in both foundational settings and as a resource for computation and security applications.
We show a purely local protocol to upgrade local realistic correlations to genuine non-local correlations if only one local party has access to a negative probabilistic bit (nebit), i.e., a bit taking 000 with probability 1+Δ1+\Delta1+Δ and 111 with probability −Δ-\Delta−Δ. The minimal amount of nebit's negativity Δ\DeltaΔ required for the upgrade can serve as a measure of non-locality. The upgrade protocol bears a striking resemblance to ordinary local unitary operations in quasi-stochastic formulations of quantum theory, mathematically equivalent to positive stochastic processes controlled by nebits. This suggests that nebits can be interpreted as units of quantum departure from classical physics as well.
A quantum system of any fixed dimension can be prepared in a continuum of states, yet it cannot be used to transmit an unlimited amount of classical information. Similarly, the correlations observed between measurement outcomes on separate parts of a shared quantum system can be stronger than classical correlations, but they cannot transmit information. These fundamental limitations suggest that the statistics observed from quantum communication and quantum correlations may admit a simulation using a finite amount of classical communication. This expectation is confirmed in the smallest nontrivial quantum dimension, with two classical bits being necessary and sufficient to exactly simulate qubit communication and all correlations between qubits. Despite significant efforts during the previous decades, this remained the only solved case. Here we resolve both problems for every quantum dimension. The solution reveals an unexpected qualitative transition starting at dimension four: no finite amount of classical communication can exactly simulate ququart communication nor all quantum correlations of two entangled ququarts, even with unlimited shared randomness. One might have expected this transition, if it existed, to appear already for qutrits. Instead, we construct an explicit protocol that exactly simulates qutrit communication using 357357357 classical bits, and consequently, all correlations of two entangled qutrits.
Abstract In K-locality networks, local hidden variables emitted from classical sources are distributed among limited observers. We explore genuine Bell locality in classical networks, where, regarding all local hidden variables as classical objects that can be perfectly cloned and spread throughout the networks, any observer can access all local hidden variables plus shared randomness. In the proposed linear and nonlinear Bell-type inequalities, there are more correlators to reveal genuine Bell locality than those in the K-locality inequalities, and their upper bounds can be specified using the probability normalization of the predetermined probability distribution. On the other hand, the no-cloning theorem limits the broadcast of quantum correlations in quantum networks. To explore genuine Bell nonlocality, the stabilizing operators play an important role in designing the segmented Bell operators and assigning the incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities tailored for the given qubit distributions in quantum networks.
In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting nonlocality, such as device-independent randomness generation and quantum key distribution. This relation between nonlocality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of nonlocality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where nnn noisy PR boxes are implemented using nnn noncommunicating pairs of devices, it is known that each PR box behaves as an independent biased coin: the min-entropy per PR box is constant with the number of copies. We show that this does not hold in more general scenarios where several noisy PR boxes are implemented from a single pair of devices, either used sequentially nnn times or producing nnn outcome bits in a single run. In this case, the min-entropy per PR box is smaller than the min-entropy of a single PR box, and it decreases as the number of copies increases.