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Local Activation of Non-locality With Negative Bits

Kelvin Onggadinata, Paweł Kurzyński, Dagomir Kaszlikowski

Published Jun 15, 2021• 0 citations
OpenAlex

Abstract

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 $0$ with probability $1+\Delta$ and $1$ with probability $-\Delta$. The minimal amount of nebit's negativity $\Delta$ 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.

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•Jan 16, 2017•0 citations
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.
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.
Nonclassicality, defined through nonpositivity of quasiprobability distributions such as the Wigner and Kirkwood-Dirac distributions, underlies key quantum advantages. We show that it can be remotely activated: local measurements by a correlated partner alone can drive a party whose reduced state is classical into a genuinely nonclassical conditional state. For two-qubit systems we obtain closed forms for the maximal single-branch effect and for its probability-weighted average under the best two-outcome projective measurement, the latter proven optimal over all measurements when the shared state carries no local bias. Local noise on the steered party, evaluated relative to its own noise-updated reference basis, can enhance the effect when non-unital and misaligned with that party's axis, whereas no unital channel ever helps. This nonclassicality is shown to unlock, for the same reference observable, anomalous weak values unavailable to the unsteered state under arbitrary postselection. An exactly solvable hybrid qubit-oscillator model shows the same mechanism generates Wigner negativity. These results identify measurement-induced steering as an operational resource for remotely activating nonclassicality.
Density matrices are the most general descriptions of quantum states, covering both pure and mixed states. Positive semidefiniteness is a physical requirement of density matrices, imposing nonnegative probabilities of measuring physical values. Separately, nonlocality is a property shared by some bipartite quantum systems, indicating a correlation of the component parts that cannot be described by local classical variables. In this work, we show that breaking the positive-semidefinite requirement and allowing states with a negative minimal eigenvalue arbitrarily close to zero, allows for the construction of states that are nonlocal under one component labelling but local when the labelling is interchanged. This is an observer-dependent nonlocality, showing the connection between nonlocal objectivism and negative quasi-probabilities.
One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.
We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing
Genuine multpartite quantum nonlocality can be quantified by the communication cost needed to reproduce the nonlocal correlation by classical communication models. This prompts the question as to how one may provide such an operational characterization for the nonclassicality of local multipartite correlations arising from genuinely quantum states possessing quantum discord. To answer this question, we consider a classical simulation protocol where one of the parties pre-share a random variable with the other parties who may also share arbitrary randomness. We demonstrate that genuine nonclassicality of local multipartite correlations is necessary for implying genuine superlocality which is the requirement for a larger dimension of the random variable in the above classical simulation protocol than that of quantum state that can generate the nonclassical correlations.