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Frontiers in Optics

Detecting nonlocal correlated errors: Bob gets caught faking a Bell-inequality violation

M. E. Feldman, G. K. Juul, S. J. van Enk, M. Beck

Published Jan 1, 2017• 0 citations
Publisher

Abstract

We demonstrate that loop state-preparation-and-measurement tomography is capable of detecting nonlocal correlated errors by catching Bob as he tries to fake a Bell-inequality violation while using nonlocal knowledge of Alice’s measurement settings.
DOI
10.1364/fio.2017.jw4a.21

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It is possible for two parties, Alice and Bob, to establish a secure communication link by sharing an ensemble of entangled particles, and then using these particles to generate a secret key. One way to establish that the particles are indeed entangled is to verify that they violate a Bell inequality. However, it might be the case that Bob is not trustworthy and wishes Alice to believe that their communications are secure, when in fact they are not. He can do this by managing to have prior knowledge of Alice's measurement device settings and then modifying his own settings based upon this information. In this case it is possible for shared particle states that must satisfy a Bell inequality to appear to violate this inequality, which would also make the system appear secure. When Bob modifies his measurement settings, however, he produces false correlations. Here we demonstrate experimentally that Alice can detect these false correlations, and uncover Bob's trickery, by using loop-state-preparation-and-measurement (SPAM) tomography. More generally, we demonstrate that loop SPAM tomography can detect false correlations (correlated errors) in a two-qubit system without needing to know anything about the prepared states or the measurements, other than the dimensions of the operators that describe them.
We have performed an experiment demonstrating that loop state-preparation-and-measurement tomography [Jackson and van Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors between the preparation and the measurement of a quantum system. Specifically, we have prepared pure and mixed states of single qubits encoded in the polarization of heralded individual photons. By performing measurements using multiple state preparations and multiple measurement device settings we are able to detect if there are any correlated errors between them, and we are also able to determine which state preparations are correlated with which measurements. This is accomplished by going around a ``loop'' in parameter space, which allows us to check for self-consistency. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures (POVMs) describing the detector are known. In cases where no correlations are found we are able to perform quantum state tomography of the polarization qubits by using knowledge of the detector POVMs, or quantum detector tomography by using knowledge of the state preparations. Note, however, that the detection of correlated errors does not require estimating any state or measurement parameters.
We experimentally demonstrate that we can detect correlated errors in a twin-field quantum key distribution (TFQKD) system by using a technique that is related to self-consistent tomography. We implement a TFQKD system based on a fiber-Sagnac loop, in which Alice and Bob encode information in the phase of weak coherent states that propagate in opposite directions around the loop. These states interfere as they exit the loop and are detected by a third party, Charlie, who reports the results of their measurements to Alice and Bob. We find that it is possible for Alice and Bob to detect correlated state-preparation and measurement errors while trusting only their own individual states, and without trusting Charlie’s measurements.
We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings, we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures describing the detectors are known. The only other needed information is experimentally measured expectation values, which are analyzed for self-consistency. This demonstrates that loop SPAM tomography is a useful technique for detecting errors that would degrade the performance of multiple-qubit quantum information processors.
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