arXiv subjects

Adán Cabello

Publications and source records attributed to Adán Cabello.

At least 37 records · Page 2Linked to original sources

arXiv2025

Generating multipartite nonlocality to benchmark quantum computers

We show that quantum computers can be used for producing large $n$-partite nonlocality, thereby providing a method to benchmark them. The main challenges to overcome are as follows: (i) The interaction topology might not allow arbitrary two-qubit gates. (ii) Noise limits the Bell violation. (iii) The number of combinations of local measurements grows exponentially with $n$. To overcome (i), we point out that graph states that are compatible with the two-qubit connectivity of the computer can be efficiently prepared. To mitigate (ii), we note that for specific graph states, there are $n$-partite Bell inequalities whose resistance to white noise increases exponentially with $n$. To address (iii) for any $n$ and any connectivity, we introduce an estimator that relies on random sampling. As a result, we propose a method for producing $n$-partite Bell nonlocality with unprecedented large $n$. This allows one, in return, to benchmark nonclassical correlations regardless of the number of qubits or the connectivity. We test our approach by using a simulation for a noisy IBM quantum computer, which predicts $n$-partite Bell nonlocality for at least $n=24$ qubits.

quant-ph↗

arXiv2025

Simplest bipartite perfect quantum strategies

A bipartite perfect quantum strategy (BPQS) allows two players who cannot communicate with each other to always win a nonlocal game. BPQSs are rare but fundamental in light of some recent results in quantum information, computation, and foundations. A more than 40-year-old open problem is how many inputs (measurement settings) a BPQS requires. A related problem is how many inputs are needed if, in addition, the quantum system has minimum dimension. A third, apparently unrelated, problem is what is the connection between BPQSs and state-independent contextuality, which inspired the first BPQSs. Here, we solve the third problem: we prove that {\em every} BPQS defines a Kochen-Specker set. We use this result to identify the BPQS with the smallest number of inputs, both in the general case and in the case of minimum dimension, and solve some related problems. We conjecture that the BPQSs presented here are the solutions to the first two problems.

quant-ph↗

arXiv2024

Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy

We show that a quantum correlation $p$ is in a face of the nonsignaling polytope with no local points if and only if $p$ has nonlocal content 1, if and only if $p$ allows for a Greenberger-Horne-Zeilinger-like proof, and if and only if $p$ provides a perfect strategy for a nonlocal game. That is, face nonsignaling (FNS) correlations, full nonlocality (FN), all-versus nothing (AVN) proofs, and pseudotelepathy (PT) are equivalent. This shows that different resources behind a wide variety of fundamental results are in fact the same resource. We demonstrate that quantum correlations with FNS=FN=AVN=PT do not need to maximally violate a tight Bell inequality. We introduce a method for identifying quantum FNS=FN=AVN=PT correlations and use it to prove quantum mechanics does not allow for FNS=FN=AVN=PT neither in the (3,3;3,2) nor in the (3,2;3,4) Bell scenarios. This solves an open problem that, due to the FNS=FN=AVN=PT equivalence, has implications in several fields.

quant-ph↗

arXiv2024

Local contextuality-based self-tests are sufficient for randomness expansion secure against quantum adversaries

In quantum cryptography, secure randomness expansion involves using a short private string of random bits to generate a longer one, even in the presence of an adversary who may have access to quantum resources. In this work, we demonstrate that local contextuality-based self-tests are sufficient to construct a randomness expansion protocol that is secure against computationally unbounded quantum adversaries. Our protocol is based on self-testing from non-contextuality inequalities and we prove that our scheme asymptotically produces secure random numbers which are $\mathcal{O}(m\sqrtε)$-close to uniformly distributed and private, where $ε$ is the robustness parameter of the self-test and $m$ is the length of the generated random bit string. Our protocol is semi-device-independent in the sense that it inherits any assumptions necessary for the underlying self-test.

quant-ph↗

arXiv2024

Perfect quantum strategies with small input cardinality

A perfect strategy is one that allows the mutually in-communicated players of a nonlocal game to win every trial of the game. Perfect strategies are basic tools for some fundamental results in quantum computation and crucial resources for some applications in quantum information. Here, we address the problem of producing qudit-qudit perfect quantum strategies with a small number of settings. For that, we exploit a recent result showing that any perfect quantum strategy induces a Kochen-Specker set. We identify a family of KS sets in even dimension $d \ge 6$ that, for many dimensions, require the smallest number of orthogonal bases known: $d+1$. This family was only defined for some $d$. We first extend the family to infinitely many more dimensions. Then, we show the optimal way to use each of these sets to produce a bipartite perfect strategy with minimum input cardinality. As a result, we present a family of perfect quantum strategies in any $(2,d-1,d)$ Bell scenario, with $d = 2^kp^m$ for $p$ prime, $m \geq k \geq 0$ (excluding $m=k=0$), $d = 8p$ for $p \geq 19$, $d=kp$ for $p > ((k-2)2^{k-2})^2$ whenever there exists a Hadamard matrix of order $k$, other sporadic examples, as well as a recursive construction that produces perfect quantum strategies for infinitely many dimensions $d$ from any dimension $d'$ with a perfect quantum strategy. We identify their associated Bell inequalities and prove that they are not tight, which provides a second counterexample to a conjecture of 2007.

quant-ph↗

arXiv2024

Lifting noncontextuality inequalities

Kochen-Specker contextuality is a fundamental feature of quantum mechanics and a crucial resource for quantum computational advantage and reduction of communication complexity. Its presence is witnessed in empirical data by the violation of noncontextuality inequalities. However, all known noncontextuality inequalities corresponding to facets of noncontextual polytopes are either Bell inequalities or refer to cyclic or state-independent contextuality scenarios. We introduce a general method for lifting noncontextuality inequalities, deriving facets of noncontextual polytopes for more complex scenarios from known facets of simpler subscenarios. Concretely, starting from an arbitrary scenario, the addition of a new measurement or a new outcome preserves the facet-defining nature of any noncontextuality inequality. This extends the results of Pironio [J. Math. Phys. 46, 062112 (2005)] from Bell nonlocality scenarios to contextuality scenarios, unifying liftings of Bell and noncontextuality inequalities. Our method produces facet-defining noncontextuality inequalities in all scenarios with contextual correlations, and we present examples of facet-defining noncontextuality inequalities for scenarios where no examples were known. Our results shed light on the structure of noncontextuality polytopes and the relationship between such polytopes across different scenarios.

quant-ph↗

arXiv2024

Certifying sets of quantum observables with any full-rank state

We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this ``certification with any full-rank state'' (CFR) is possible for any quantum system of finite dimension $d \ge 3$ and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.

quant-ph↗

arXiv2024

Long-distance entanglement sharing using hybrid states of discrete and continuous variables

We introduce a feasible scheme to produce high-rate long-distance entanglement which uses hybrid entanglement (HE) between continuous variables (CV) and discrete variables (DV). We show that HE can effectively remove the experimental limitations of existing CV and DV systems to produce long range entanglement. We benchmark the resulting DV entangled states using an entanglement-based quantum key distribution (EB-QKD) protocol. We show that, using HE states, EB-QKD is possible with standard telecommunication fibers for 300 km. The key idea is using the CV part, which can be adjusted to be robust against photon losses, for increasing the transmission distance, while using the DV part for achieving high secure key rates. Our results point out that HE states provide a clear advantage for practical long-distance and high-rate entanglement generation that may lead to further applications in quantum information processing.

quant-ph↗

arXiv2024

The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios

A necessary condition for the probabilities of a set of events to exhibit Bell nonlocality or Kochen-Specker contextuality is that the graph of exclusivity of the events contains induced odd cycles with five or more vertices, called odd holes, or their complements, called odd antiholes. From this perspective, events whose graph of exclusivity are odd holes or antiholes are the building blocks of contextuality. For any odd hole or antihole, any assignment of probabilities allowed by quantum mechanics can be achieved in specific contextuality scenarios. However, here we prove that, for any odd hole, the probabilities that attain the quantum maxima cannot be achieved in Bell scenarios. We also prove it for the simplest odd antiholes. This leads us to the conjecture that the quantum maxima for any of the building blocks cannot be achieved in Bell scenarios. This result sheds light on why the problem of whether a probability assignment is quantum is decidable, while whether a probability assignment within a given Bell scenario is quantum is, in general, undecidable. This also helps to undertand why identifying principles for quantum correlations is simpler when we start by identifying principles for quantum sets of probabilities defined with no reference to specific scenarios.

quant-ph↗

arXiv2024

Loophole-free Bell tests with randomly chosen subsets of measurement settings

There are bipartite quantum nonlocal correlations requiring very low detection efficiency to reach the loophole-free regime but that need too many measurement settings to be practical for actual experiments. This leads to the general problem of what can be concluded about loophole-free Bell nonlocality if only a random subset of these settings is tested. Here we develop a method to address this problem. We show that, in some cases, it is possible to detect loophole-free Bell nonlocality testing only a small random fraction of the settings. The prize to pay is a higher detection efficiency. The method allows for a novel approach to the design of loophole-free Bell tests in which, given the dimension of the local system, the visibility, and the detection efficiency available, one can calculate the fraction of the contexts needed to reach the detection-loophole-free regime. The results also enforce a different way of thinking about the costs of classically simulating quantum nonlocality, as it shows that the amount of resources that are needed can be made arbitrarily large simply by considering more contexts.

quant-ph↗

arXiv2023

Experimental test of high-dimensional quantum contextuality based on contextuality concentration

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality ``concentrates'' as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

quant-ph↗

arXiv2023

Optimal and tight Bell inequalities for state-independent contextuality sets

Two fundamental quantum resources, nonlocality and contextuality, can be connected through Bell inequalities that are violated by state-independent contextuality (SI-C) sets. These Bell inequalities allow for applications that require simultaneous nonlocality and contextuality. However, for existing Bell inequalities, the nonlocality produced by SI-C sets is very sensitive to noise. This precludes experimental implementation. Here we identify the Bell inequalities for which the nonlocality produced by SI-C sets is optimal, i.e., maximally robust to either noise or detection inefficiency, for the simplest SI-C [S. Yu and C. H. Oh, Phys. Rev. Lett. 108, 030402 (2012)] and Kochen-Specker sets [A. Cabello et al., Phys. Lett. A 212, 183 (1996)] and show that, in both cases, nonlocality is sufficiently resistant for experiments. Our work enables experiments that combine nonlocality and contextuality and therefore paves the way for applications that take advantage of their synergy.

quant-ph↗

arXiv2023

Quantum contextuality provides communication complexity advantage

Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimensions producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device-independent protocol for quantum key distribution.

quant-ph↗

arXiv2023

Certification of genuine time-bin and energy-time entanglement with integrated photonics

Time-bin (TB) and energy-time (ET) entanglement are crucial resources for long-distance quantum information processing. Recently, major efforts have been made to produce compact high-quality sources of TB/ET entangled photons based on solid-state integrated technologies. However, these attempts failed to close the so-called "post-selection loophole". Here, we present an integrated photonic general Bell-test chip for genuine (i.e., free of the post-selection loophole) TB and ET entanglement certification. We report a violation of a Bell inequality by more than 10 standard deviations using our device based on the "hug" interferometric scheme. The experiment also demonstrates that the hug scheme, previously exploited for ET entanglement, can also be used for genuine TB entanglement.

quant-ph↗

arXiv2023

Graph-theoretic approach to Bell experiments with low detection efficiency

Bell inequality tests where the detection efficiency is below a certain threshold $η_{\rm{crit}}$ can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low $η_{\rm{crit}}$ and relatively low dimension $d$ of the local quantum systems. The method has two steps. First, we show a family of bipartite Bell inequalities for which, for correlations produced by maximally entangled states, $η_{\rm{crit}}$ can be upper bounded by a function of some invariants of graphs, and use it to identify correlations that require small $η_{\rm{crit}}$. We present examples in which, for maximally entangled states, $η_{\rm{crit}} \le 0.516$ for $d=16$, $η_{\rm{crit}} \le 0.407$ for $d=28$, and $η_{\rm{crit}} \le 0.326$ for $d=32$. We also show evidence that the upper bound for $η_{\rm{crit}}$ can be lowered down to $0.415$ for $d=16$ and present a method to make the upper bound of $η_{\rm{crit}}$ arbitrarily small by increasing the dimension and the number of settings. All these upper bounds for $η_{\rm{crit}}$ are valid (as it is the case in the literature) assuming no noise. The second step is based on the observation that, using the initial state and measurement settings identified in the first step, we can construct Bell inequalities with smaller $η_{\rm{crit}}$ and better noise robustness. For that, we use a modified version of Gilbert's algorithm that takes advantage of the automorphisms of the graphs used in the first step. We illustrate its power by explicitly developing an example in which $η_{\rm{crit}}$ is $12.38\%$ lower and the required visibility is $14.62\%$ lower than the upper bounds obtained in the first step. The tools presented here may allow for developing high-dimensional loophole-free Bell tests and loophole-free Bell nonlocality over long distances.

quant-ph↗

arXiv2023

Kochen-Specker Contextuality

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

quant-ph↗

arXiv2022

Irreducible magic sets for $n$-qubit systems

Magic sets of observables are minimal structures that capture quantum state-independent advantage for systems of $n\ge 2$ qubits and are, therefore, fundamental tools for investigating the interface between classical and quantum physics. A theorem by Arkhipov (arXiv:1209.3819) states that $n$-qubit magic sets in which each observable is in exactly two subsets of compatible observables can be reduced either to the two-qubit magic square or the three-qubit magic pentagram [N. D. Mermin, Phys. Rev. Lett. 65, 3373 (1990)]. An open question is whether there are magic sets that cannot be reduced to the square or the pentagram. If they exist, a second key question is whether they require $n >3$ qubits, since, if this is the case, these magic sets would capture minimal state independent quantum advantage that is specific for $n$-qubit systems with specific values of $n$. Here, we answer both questions affirmatively. We identify magic sets which cannot be reduced to the square or the pentagram and require $n=3,4,5$, or $6$ qubits. In addition, we prove a generalized version of Arkhipov's theorem providing an efficient algorithm for, given a hypergraph, deciding whether or not it can accommodate a magic set, and solve another open problem, namely, given a magic set, obtaining the tight bound of its associated noncontextuality inequality.

quant-ph↗

arXiv2022

Quantum nonlocality: How does nature do it?

In a recent note, Hance and Hossenfelder (arXiv:2211.01331) recall that "locally causal completions of quantum mechanics are possible, if they violate the assumption [called statistical independence or measurement independence] that the hidden variables do not in any way depend on measurement settings" and that, consequently, the experimental violations of Bell inequalities "show that maintaining local causality requires violating statistical independence". However, Hance and Hossenfelder also argue that "we should (...) look for independent experimental evidence that can distinguish the two different options: non-locality and statistical independence, or locality and violations of statistical independence" and that "the unwillingness to consider theories without statistical independence may be the reason we do not yet have a locally causal theory for the foundations of physics that is consistent with general relativity". Here, we recall that there is a third option, namely, rejecting that measurement outcomes are governed in any way by hidden variables. Moreover, we argue that some recent results in the search for principles singling out the sets of quantum correlations for Bell and Kochen-Specker contextuality scenarios point out that this third option is scientifically more plausible and answers the question of why and how nature produces quantum nonlocality.

quant-ph↗