arXiv subjects

Adán Cabello

Publications and source records attributed to Adán Cabello.

At least 19 recordsLinked to original sources

arXiv2026

SAT + NAUTY: Orderly Generation of Small Kochen-Specker Sets Containing the Smallest State-independent Contextuality Set

We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent contextuality. To enable this search, we introduce a novel SAT-based orderly generation framework integrating recursive canonical labeling (RCL) with the graph isomorphism tool NAUTY. We demonstrate that previous SAT approaches relying on lexicographical canonicity suffer from exponential scaling on canonical graphs. This limitation renders them intractable on the large instances (25 to 33 vertices) encountered in our search, whereas our RCL check maintains consistent millisecond-level performance, effectively eliminating the bottleneck. Overcoming this bottleneck allows us to perform the first exhaustive enumeration of all KS sets with up to 33 rays containing the complete 25-ray state-independent contextuality (SI-C) set obtained by rigid extensions of the Yu-Oh set in 1,641 CPU hours. We found and verified that the 33-ray set discovered by Schütte is the smallest three-dimensional KS set containing the complete 25-ray SI-C set. All non-existence results are backed by independently verifiable proof certificates via an extension of the DRAT proof format.

cs.LO↗

arXiv2026

Exponentially decreasing critical detection efficiency for any Bell inequality

We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $η$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.

quant-ph↗

arXiv2026

Exploring Bell Nonlocality with Extremal Non-Signaling Boxes

Extremal non-signaling (ENS) boxes are correlations that correspond to vertices of the non-signaling polytope of a Bell scenario. Neither quantum theory nor any theory for ideal measurements allows for ENS boxes. That is, according to quantum theory, ENS boxes are nonphysical. Still, ENS boxes are crucial for addressing a number of problems in Bell nonlocality. Here, we obtain ENS boxes in arbitrary bipartite Bell scenarios and present the complete list of ENS boxes for several unexplored scenarios. Equipped with the boxes, we revisit several foundational questions. We find that already two copies of any ENS box violate the exclusivity (or local orthogonality) and Specker's principles. We provide the minimal decomposition of the magic square correlation - the simplest known perfect correlation in nature - in terms of ENS boxes. We identify the minimal scenario in which a dit of communication (with d < 6) is insufficient to simulate ENS boxes. Our results show that the ENS boxes approach leads to new results and opens new avenues for research.

quant-ph↗

arXiv2026

Experimental Certification of Quantum Measurements with Maximally Mixed States

So far, certifying quantum devices from their input-output statistics, under minimal assumptions, required the preparation of specific pure quantum states. Recently, Xu et al. [Phys. Rev. Lett. 132, 140201 (2024)] have demonstrated that certain sets of quantum observables can be certified using any state of full rank. However, their method is restricted to ideal conditions. Here, we address this problem and present an experimentally robust method that eliminates the need of preparing states with high fidelity with respect to specific pure states. We demonstrate the feasibility of the method by experimentally certifying photonic devices implementing Peres' set of 24 ququart observables [J. Phys. A 24, L175 (1991)] and Yu and Oh's set of 13 qutrit observables [Phys. Rev. Lett. 108, 030402 (2012)], using maximally mixed states as input. This approach offers a crucial advantage for certifying high-dimensional quantum systems, since it works with maximally mixed and thermal states.

quant-ph↗

arXiv2025

The simplest Kochen-Specker set

Kochen-Specker (KS) sets are fundamental in physics. Every time nature produces bipartite correlations attaining the nonsignaling limit, or two parties always win a nonlocal game impossible to always win classically, is because the parties are measuring a KS set. The simplest quantum system in which all these phenomena occur is a pair of three-level systems. However, the simplest KS sets in dimension three known are asymmetrical and require a large number of bases (the current minimum is 16, set by Peres and Penrose). Here we present a KS set that is much more symmetrical and easier to prove than any previous example. It sets a new record for minimum number of bases, 14, and enables us to refute Conjecture 2 in Phys. Rev. Lett. 134, 010201 (2025), setting a new record for qutrit-qutrit perfect strategies with a minimum number of inputs: 5-9. We establish the fundamental nature of this set in quantum theory.

quant-ph↗

arXiv2025

Contextuality-based quantum key distribution with deterministic single-photon sources

Photons are central to quantum technologies, with photonic qubits offering a promising platform for quantum communication. Semiconductor quantum dots stand out for their ability to generate single photons on demand, a key capability for enabling long-distance quantum networks. In this work, we utilize high-purity single-photon sources based on self-assembled InAs(Ga)As quantum dots as quantum information carriers. We demonstrate that such on-demand single photons can generate quantum contextuality. This capability enables a novel protocol for semi-device-independent quantum key distribution over free-space channels. Crucially, our method does not require ideal or perfectly projective measurements, opening a new pathway for robust and practical quantum communication.

quant-ph↗

arXiv2025

Supersinglets can be self-tested with perfect quantum strategies

Supersinglets are states of spin-zero of $d \ge 3$ particles of $d$ levels. They are invariant under unitary transformations of the form $U^{\otimes d}$ and have applications in metrology, error protection, and communication. They also violate some specific Bell inequalities. However, none any of these applications {\em require} supersinglets nor do any of these Bell inequality violations capture the unique properties of the supersinglets. This leads to two questions. Question 1 is whether there exists a task that can be solved only with supersinglets. Question 2 is whether supersinglets can produce a unique $d$-partite, $d$-dimensional nonlocal signature. We answer both questions affirmatively by presenting a protocol that self-test all supersinglets by producing $d$-partite, $d$-dimensional {\em perfect} quantum strategies for any $d \ge 3$.

quant-ph↗

arXiv2025

Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption

Recent results show that Kochen-Specker (KS) sets of observables are fundamental to quantum information, computation, and foundations beyond previous expectations. Among KS sets, those that are unique up to unitary transformations (i.e., "rigid") are especially important. The problem is that we do not know any rigid KS set in $\mathbb{C}^3$, the smallest quantum system that allows for KS sets. Moreover, none of the existing methods for constructing KS sets leads to rigid KS sets in $\mathbb{C}^3$. Here, we show that two fundamental structures of quantum theory define two rigid KS sets. One of these structures is the super-symmetric informationally complete positive-operator-valued measure. The other is the minimal state-independent contextuality set. The second construction provides a clue to solve the minimal KS problem, the most important open problem in this field. We prove that there is no KS set of 30 elements that can be obtained from the minimal state-independent contextuality set by completing bases and adding elements that are orthogonal to two previous elements. We conjecture that 31 is the solution to the minimal KS set problem.

quant-ph↗

arXiv2025

Possible consequences for physics of the negative resolution of Tsirelson's problem

In 2020, Ji et al. [arXiv:2001.04383 and Comm.~ACM 64}, 131 (2021)] provided a proof that the complexity classes $\text{MIP}^\ast$ and $\text{RE}$ are equivalent. This result implies a negative resolution of Tsirelson's problem, that is, $C_{qa}$ (the closure of the set of tensor product correlations) and $C_{qc}$ (the set of commuting correlations) can be separated by a hyperplane (that is, a Bell-like inequality). In particular, there are correlations produced by commuting measurements (a finite number of them and with a finite number of outcomes) on an infinite-dimensional quantum system which cannot be approximated by sequences of finite-dimensional tensor product correlations. Here, we point out that there are four logical possibilities of this result. Each possibility is interesting because it fundamentally challenges the nature of spacially separated systems in different ways. We list open problems for making progress for deciding which of the possibilities is correct.

quant-ph↗

arXiv2025

Memory cost of quantum contextuality with Pauli observables

Classically simulating the quantum contextual correlations produced by sequences of ideal measurements of compatible observables requires the measured system to have an internal memory. Computing the minimum amount of memory needed is, in general, challenging. Here, building upon the work of Kleinmann et al. [New J. Phys. 13, 113011 (2011)], we prove that the memory cost for simulating the contextuality produced by the $10$ three-qubit observables of Mermin's pentagram is only $\log_2(5) \approx 2.32$ bits, but the memory cost for simulating the contextuality produced by all $15$ two-qubit Pauli observables is, at least, $\log_2(6) \approx 2.58$ bits, thus exceeding the classical capacity of the system on which the measurements are performed. We also add results on the memory for simulating some subsets of quantum predictions.

quant-ph↗

arXiv2025

Minimum optical depth multiport interferometers for approximating arbitrary unitary operations and pure states

Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers, approximating with a given infidelity any pure state preparation and any unitary operation. By means of numerical calculations, we show that pure states, in any dimension $d$, can be prepared with infidelity $\le 10^{-15}$ with three layers of $d$ dimensional Fourier transforms and three layers of configurable phase shifters. We also present numerical evidence that $d+1$ layers of $d$-dimensional Fourier transforms and $d+2$ layers of configurable phase shifters can produce any unitary operation with infidelity $\le 10^{-14}$. The conclusions are achieved by numerical simulations in the range from $d = 3$ to $d=10$. These results are interesting in light of the recent availability of multicore fiber-integrated multiport interferometers.

quant-ph↗

arXiv2025

How to avoid (apparent) signaling in Bell tests

Bell tests have become a powerful tool for quantifying security, randomness, entanglement, and many other properties, as well as for investigating fundamental physical limits. In all these cases, the specific experimental value of the Bell parameter is important as it leads to a quantitative conclusion. However, experimental implementations can also produce experimental data with (apparent) signaling. This signaling can be attributed to systematic errors occurring due to weaknesses in the experimental designs. Here we point out the importance, for quantitative applications, to identify and address this problem. We present a set of experiments with polarization-entangled photons in which we identify common sources of systematic errors and demonstrate approaches to avoid them. In addition, we establish the highest experimental value for the Bell-CHSH parameter obtained after applying strategies to minimize signaling that we are aware of: $S = 2.812 \pm 0.003$ and negligible systematic errors. The experiments did not randomize the settings and did not close the locality loophole.

quant-ph↗

arXiv2025

Test of the physical significance of Bell nonlocality

Loophole-free violations of Bell inequalities imply that at least one of the assumptions behind local hidden-variable theories must fail. Here, we show that, if only one fails, then it has to fail completely, therefore excluding models that partially constrain freedom of choice or allow for partial retrocausal influences, or allow partial instantaneous actions at a distance. Specifically, we show that (i) any hidden-variable theory with outcome independence (OI) and arbitrary joint relaxation of measurement independence (MI) and parameter independence (PI) can be experimentally excluded in a Bell-like experiment with many settings on high-dimensional entangled states, and (ii) any hidden-variable theory with MI, PI and arbitrary relaxation of OI can be excluded in a Bell-like experiment with many settings on qubit-qubit entangled states.

quant-ph↗

arXiv2025

Energy-time and time-bin entanglement: past, present and future

Entanglement is a key resource in many quantum information tasks. From a fundamental perspective entanglement is at the forefront of major philosophical discussions advancing our understanding of nature. An experimental scheme was proposed in 1989 by Franson that exploited the unpredictability in the generation time of a photon pair in order to produce a then new form of quantum entanglement, known as energy-time entanglement. A later modification gave rise to the very popular time-bin entanglement, an important cornerstone in many real-world quantum communication applications. Both forms of entanglement have radically pushed forward our understanding of quantum mechanics throughout the 1990s and 2000s. A decade later modifications to the original proposals were proposed and demonstrated, which opens the path for the highly sought-after device-independence capability for entanglement certification, with a goal of ultra-secure quantum communication. In this review we cover the beginnings of energy-time and time-bin entanglement, many key experiments that expanded our understanding of what was achievable in quantum information experiments all the way down to modern demonstrations based on new technological advances. We will then point out to the future discussing the important place that energy-time and time-bin entanglement will have in upcoming quantum networks and novel protocols based on nonlocality.

quant-ph↗

arXiv2025

Reply to Pavičić's 'Comment on "Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies"' (arXiv:2502.13787)

According to Paviči{ć}, Kochen and Specker's 117-observable set is not a ``Kochen-Specker set''. By the same reason, in arXiv:2502.13787, Paviči{ć} claims that 10 statements in our paper ``Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies'' [Phys. Rev. A 111, 022408 (2025)] are ``wrong''. In all cases, Paviči{ć}'s claims are based on the fact that he is assuming a different definition of Kochen-Specker (KS) set. Adopting a terminology used by, e.g., Larsson, the sets that Paviči{ć} call KS sets can be called ``extended'' KS sets, since they are constructed by adding observables to the ``original'' KS sets. For example, Paviči{ć} adds 75 observables to the original 117-observable KS set. Beyond terminology, there are fundamental physical reasons for focusing on the original KS sets. One reason is that, for experimentally observing quantum state-independent contextuality, there is no need to measure the observables added in the extended sets. Another reason is that, to produce bipartite perfect quantum strategies, or correlations in a face of the nonsignaling polytope with no local points, or correlations with nonlocal content 1, the two parties do not need to measure any of the observables added in the extended sets. We also respond to other claims made by Paviči{ć} about our work.

quant-ph↗

arXiv2025

Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies

Bipartite perfect quantum strategies (BPQSs) allow two players isolated from each other to win every trial of a nonlocal game. BPQSs have crucial roles in recent developments in quantum information and quantum computation. However, only few BPQSs with a small number of inputs are known and only one of them has been experimentally tested. It has recently been shown that every BPQS has an associated Kochen-Specker (KS) set. Here, we first prove that any BPQS of minimum input cardinality that can be obtained from a generalized KS set can also be obtained from a KS set of pure states. Then, we address the problem of finding BPQSs of small input cardinality starting from KS sets. We introduce an algorithm that identifies the BPQS with the minimum number of settings for any given KS set. We apply it to many well-known KS sets of small cardinality in dimensions 3, 4, 5, 6, 7, and 8. In each dimension, the algorithm either recovers the best BPQS known or find one with fewer inputs.

quant-ph↗

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↗