arXiv subjects

Peter Bierhorst

Publications and source records attributed to Peter Bierhorst.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Advantage over Wirings of Nonsignaling Boxes in Multipartite Networks

Quantum-entangled measurements are known to enable multi-party behaviors that are impossible with unentangled measurements on nonlocal resources, even those that are super-quantum and bound only by the no-signaling principle. This advantage can be witnessed by the entanglement swapping protocol, along with corresponding impossibility results for "nonlocality swapping". However, the advantage assumes the absence of pre-existing nonlocal resources shared by the swapped-to parties; it no longer holds if all pairs of parties are allowed to share bipartite nonlocal resources. Here, we consider a resource-theoretic perspective in which bipartite nonclassical resources are free resources that can be shared by any pair of parties in a multipartite network, and ask whether quantum entangled measurements can still provide an advantage over certain basic measurements, known as wirings, of nonsignaling nonlocal resources. We resolve this question in the affirmative by demonstrating an explicit four-party behavior that can be achieved with bipartite quantum resources subject to entangled measurements, and cannot be achieved if the bipartite resources are allowed to be more general nonsignaling nonlocal "boxes" so long as the measurements are restricted to local wirings, even also allowing for globally shared classical randomness. Furthermore, the argument generalizes: the same separation can be witnessed for K+2 parties with access to K-partite nonlocal resources for any K > 2. We also examine these results in different contexts, such as the star network configurations and scenarios not admitting globally shared classical randomness, further enhancing understanding of the capabilities of entangled measurements in multi-party configurations.

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arXiv2026

Intractability of Witnessing Entangled Measurements Device Independently

Protocols have been previously proposed to certify the presence of an entangled measurement in a fully device-independent manner. Here, I provide models for these protocols in which the claimed measurement is not entangled, and demonstrate it is always possible to displace entanglement from measurements to measured states for a general class of device-independent scenarios. This indicates that no black-box measurement scenario requires entangled measurements to replicate its behavior, which is relevant to our fundamental understanding of this phenomenon and how to witness it.

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arXiv2025

Quantitative and Optimal Device-Independent Lower Bounds on Detection Efficiency

This paper examines a quantitative and optimal lower bound on the detector efficiency in a (2,2,2) Bell experiment within a fully device-independent framework, whereby the detectors used in the experiment are uncharacterized. We provide a tight lower bound on the minimum efficiency required to observe a desired Bell-CHSH violation using the Navascu\'es-Pironio-Ac\'in (NPA) hierarchy, confirming tightness up to four decimal places with numerical optimization over explicit quantum realizations. We then introduce the effect of dark counts and demonstrate how to quantify the minimum required efficiency to observe a desired CHSH violation with an increasing dark count error. Finally, to obtain an analytical closed-form expression of the minimum efficiency, we consider the set of no-signaling behaviors that satisfy the Tsirelson bound, which are easier to characterize than the quantum set. Using such behaviors, we find a simple closed-form expression for a lower bound on the minimum efficiency which is monotonically increasing with the CHSH violation, though the analytically obtained lower bounds are meaningfully below the numerically tight lower bound.

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arXiv2025

No-signalling-projection-invariant Bell inequalities

In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the $L^2$-projection of weakly signalling data onto the no-signalling polytope leaves the violation of this canonical Bell inequality unchanged. Our methods allow us to derive a general closed formula for the projection and present a substantially more computationally simple procedure for its evaluation. We also show this can be generalised to non-standard projections of potential interest for certain applications. No-signalling projections serve as a preliminary step before undertaking any device-independent application involving Bell experiment data, such as hypothesis testing against local realism, random number generation and entanglement detection.

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arXiv2025

Consistency and Causality of Interconnected Nonsignaling Resources

This paper examines networks of $n$ measuring parties sharing $m$ nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of (3,2,2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al. [Phys. Rev. Lett. 129:150401 (2022)]

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arXiv2024

Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement

In this work, we introduce multipartite intrinsic non-locality as a method for quantifying resources in the multipartite scenario of device-independent (DI) conference key agreement. We prove that multipartite intrinsic non-locality is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for two variants of multipartite mutual information, which we then use to prove that multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing the main result of our paper: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement. We discuss various examples of DI conference key protocols and compare our upper bounds for these protocols with known lower bounds. Finally, we calculate upper bounds on recent experimental realizations of DI quantum key distribution.

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arXiv2024

Strength of statistical evidence for genuine tripartite nonlocality

Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio (PBR) protocol to analyse finite experimental data and quantify the strength of evidence in favour of genuine tripartite nonlocality in terms of a valid $p$-value. In our work, we propose an efficient modification of the test factor optimisation using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigour.

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arXiv2023

A Hierarchy of Multipartite Nonlocality and Device-Independent Effect Witnesses

According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multi-partite measurement scenario (3 parties, 2 measurement settings, and 2 outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources -- thus witnessing the most general form of GMNL -- but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.

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arXiv2023

Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework

The Probability Estimation Framework involves direct estimation of the probability of occurrences of outcomes conditioned on measurement settings and side information. It is a powerful tool for certifying randomness in quantum non-locality experiments. In this paper, we present a self-contained proof of the asymptotic optimality of the method. Our approach refines earlier results to allow a better characterisation of optimal adversarial attacks on the protocol. We apply these results to the (2,2,2) Bell scenario, obtaining an analytic characterisation of the optimal adversarial attacks bound by no-signalling principles, while also demonstrating the asymptotic robustness of the PEF method to deviations from expected experimental behaviour. We also study extensions of the analysis to quantum-limited adversaries in the (2,2,2) Bell scenario and no-signalling adversaries in higher $(n,m,k)$ Bell scenarios.

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arXiv2021

Ruling out Bipartite Nonsignaling Nonlocal Models for Tripartite Correlations

Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so-obtained correlations, such as no-signaling, indeed hold, and show how to use the framework to derive Bell-inequality-type constraints on these correlations that can be robustly violated by tripartite quantum systems. In particular, we use this framework to rederive a version of one such constraint previously described in a paper of Chao and Reichardt (arXiv:1706.02008).

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arXiv2021

Scalable multiphoton quantum metrology with neither pre- nor post-selected measurements

The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric down-conversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling and quantum networks.

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arXiv2020

Tsirelson Polytopes and Randomness Generation

We classify the extreme points of a polytope of probability distributions in the (2,2,2) CHSH-Bell setting that is induced by a single Tsirelson bound. We do the same for a class of polytopes obtained from a parametrized family of multiple Tsirelson bounds interacting non-trivially. Such constructions can be applied to device-independent random number generation using the method of probability estimation factors [Phys. Rev. A, 98:040304(R), 2018]. We demonstrate a meaningful improvement in certified randomness applying the new polytopes characterized here.

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arXiv2018

Certifying Quantum Randomness by Probability Estimation

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation can take advantage of verifiable physical constraints, and the certification is with respect to classical side information. Examples include randomness from single-photon measurements and device-independent randomness from Bell tests. Advantages of probability estimation include adaptability to changing experimental conditions, unproblematic early stopping when goals are achieved, optimal randomness rates, applicability to Bell tests with small violations, and unsurpassed finite-data efficiency. We greatly reduce latencies for producing random bits and formulate an associated rate-tradeoff problem of independent interest. We also show that the latency is determined by an information-theoretic measure of nonlocality rather than the Bell violation.

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arXiv2018

Quantum Randomness Generation by Probability Estimation with Classical Side Information

We develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can stop performing trials early, as soon as the desired amount of randomness is extractable. It can be used with arbitrary, partially known and time-dependent probabilities for the random settings choices. Furthermore, it is suitable for application to experimental configurations with low Bell violation per trial, such as current optical loophole-free Bell tests. It is possible to adapt to time-varying experimental parameters. We formulate the framework for the general situation where the trial probability distributions are constrained to a known set. Randomness expansion with logarithmic settings entropy is possible for many relevant configurations. We implement probability estimation numerically and apply it to a representative settings-conditional probability distribution of the outcomes from an atomic loophole-free Bell test [Rosenfeld et al., Phys. Rev. Lett. 119:010402 (2017), arXiv:1611.04604 (2016)] to illustrate trade-offs between the amount of randomness, error, settings entropy, unknown settings biases, and number of trials. We then show that probability estimation yields more randomness from the loophole-free Bell-test data analyzed in [Bierhorst et al., arXiv:1702.05178 (2017)] and tolerates adversarial settings probability biases.

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arXiv2018

Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within $10^{-12}$. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

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arXiv2017

Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

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arXiv2016

A strong loophole-free test of local realism

We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p-values as small as $5.9\times 10^{-9}$ for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p-value is $2.3 \times 10^{-7}$. We therefore reject the hypothesis that local realism governs our experiment.

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arXiv2016

Geometric Decompositions of Bell Polytopes with Practical Applications

In the well-studied (2,2,2) Bell experiment consisting of two parties, two measurement settings per party, and two possible outcomes per setting, it is known that if the experiment obeys no-signaling constraints, then the set of admissible experimental probability distributions is fully characterized as the convex hull of 24 distributions: 8 Popescu-Rohrlich (PR) boxes and 16 local deterministic distributions. Here, we refine this result to show that in the (2,2,2) case, any nonlocal nonsignaling distribution can always be uniquely expressed as a convex combination of exactly one PR box and (up to) eight local deterministic distributions. In this representation each PR box will always occur only with a fixed set of eight local deterministic distributions with which it is affiliated. This decomposition has multiple applications: we demonstrate an analytical proof that the minimum detection efficiency for which nonlocality can be observed is $η>2/3$ even for theories constrained only by the no-signaling principle, and we develop new algorithms that speed the calculation of important statistical functions of Bell test data. Finally, we enumerate the vertices of the no-signaling polytope for the (2, n, 2) "chained Bell" scenario and find that similar decomposition results are possible in this general case. Here, our results allow us to prove the optimality of a bound, derived in Barrett et al. [1], on the proportion of local theories in a local/nonlocal mixture that can be inferred from the experimental violation of a chained Bell inequality.

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