arXiv subjects

Remigiusz Augusiak

Publications and source records attributed to Remigiusz Augusiak.

At least 19 recordsLinked to original sources

arXiv2026

Device-independent certification of tripartite quantum networks with bilocal Bell inequalities

While quantum networks have been extensively studied as a natural extension of the standard Bell scenario with a richer correlation structure, general constructions of nonlinear Bell inequalities with self-testing properties are still largely lacking. In this work, we present a general method for constructing such inequalities in the simplest network scenario, in which two independent sources distribute bipartite quantum states to three spatially separated observers. These inequalities allow for arbitrary numbers of binary measurements and are maximally violated by maximally entangled states of the corresponding local dimensions together with sets of pairwise anticommuting Clifford observables. Importantly, their maximal quantum values can be determined analytically, which makes them particularly promising for device-independent applications. In particular, we prove that these Bell inequalities can be used to device-independently certify the underlying quantum network, including both the quantum states produced by the sources and the observables measured by all parties. To the best of our knowledge, this is the first self-testing result for quantum networks that relies solely on the maximal violation of a nonlocality witness.

quant-ph↗

arXiv2026

Bell inequalities tailored to optimal global randomness certification

We present two novel families of bipartite Bell inequalities designed to achieve optimal global randomness certification for an arbitrary number of outputs $d$. We first use symmetry arguments to argue that their maximal quantum violations certify $2\log d$ random bits. For the first family, we construct a quantum realization using $d\times d$ maximally entangled states which provides a quantum violation that we conjecture to be optimal for any $d$. It is then numerically shown that the obtained quantum violation certifies optimal global randomness, up to numerical precision, for $d=3,4$. For the second family, we provide the optimal quantum violation and its quantum realization for any $d$, again using $d\times d$ maximally entangled states and projective measurements over at least two unbiased bases on one of the parties. We self-test this realization for $d=3$, which implies the optimal certification of two fully random trits.

quant-ph↗

arXiv2026

Maximal global device-independent randomness from projective measurements in every dimension

Device-independent random number generation (DIQRNG) is the most secure form of generating private randomness using quantum physical processes. Its strength lies in producing numbers that are impossible to predict by any eavesdropper restricted by the laws of quantum theory. Moreover, security is proven solely from observed measurement statistics, without the need to characterise or trust the devices used in random number generation. Implementing DIQRNG is, however, costly, as it requires high-quality entangled systems. It is therefore important to make the best use of available resources. In this work, we show that using projective measurements -- which are most readily implementable experimentally -- one can certify $2\log(d)$ bits of device-independent randomness from a bipartite system of local dimension $d$ for every $d \ge 2$, thus reaching the theoretically maximum possible rate of DIQRNG. We provide explicit protocols reaching $2\log(d)$ bits based on mutually unbiased bases. Furthermore, we compute numerical bounds on the rate for the case of imperfect implementations, showing that our protocols are robust to experimental noise.

quant-ph↗

arXiv2026

Noise robustness of three outcome Bell certified quantum randomness

We investigate device-independent certification of global randomness based on Bell inequality violations in bipartite scenarios with three outcomes per party. Our goal is to determine whether multi-outcome measurements allow one to surpass the amount of randomness achievable with binary outputs in realistic scenarios. We begin by analyzing several known Bell expressions and evaluating their robustness against noise for randomness certification. We then introduce a systematic method for generating new Bell expressions within structured families and perform a large-scale numerical study. We find that a substantial number of inequalities certify significant amounts of min-entropy. In particular, we identify simple inequalities that achieve near-maximal global randomness while involving a reduced number of measurement settings, thus improving the balance between certified randomness and number of inputs. Moreover, the vast majority of nontrivial certificates exhibit robustness against realistic noise, maintaining positive certified randomness away from the ideal regime. These results demonstrate that strong device-independent randomness expansion in multi-outcome scenarios is not restricted to carefully engineered inequalities, but arises generically within suitably constructed families of Bell expressions.

quant-ph↗

arXiv2026

All pure entangled states can lead to fully nonlocal correlations

It is a well-established fact that some quantum correlations can be nonlocal, meaning that they cannot be described by a local hidden variable model. Certain quantum correlations have a form of nonlocality so strong that they cannot be reproduced even by models having an arbitrarily small local hidden variable component. These correlations are called fully nonlocal and lead to Bell inequalities in which the maximum quantum value saturates the non-signaling bound. A well-known example of this effect, which is also referred to as quantum pseudo-telepathy or all-versus-nothing proofs of nonlocality, is the quantum distribution fulfilling the Peres-Mermin square, in which the underlying state is a $4\times4$ dimensional maximally entangled state. Other examples of full nonlocality are known but, so far, all of them are for maximally entangled states and it is an open question whether maximal entanglement is necessary for full nonlocality. In this work, we first establish a link between full nonlocality and the concept of antidistinguishability of quantum states. We use this connection to show that in every bipartite $d\times d$ Hilbert space, with $d\geq3$, there are non-maximally entangled states that are fully nonlocal. In fact, we derive simple sufficient conditions for full nonlocality that are only based on the smallest and largest Schmidt coefficients. We also show that in every dimension there exist pure entangled states that do not exhibit full nonlocality. Finally, we show that all pure entangled states can be activated to show full nonlocality in the many-copy scenario.

quant-ph↗

arXiv2026

On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions

We demonstrate that absolutely maximally entangled (AME) states consisting of $N=4n$ qudits with $n\in\{1,2,3,...\}$, each of even local dimension, cannot be realized as graph states. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. In particular, this study provides an independent solution of the recently discussed case of the AME state of four quhexes and clarifies its characterization within the stabilizer formalism, complementing the results found recently in [H. Cha, arXiv:2603.13442]. At the same time, we provide a general construction for mixed $k$-uniform states whose purity is determined by the optimal stabilizer representations. For the specific case of $(N=4,d=6)$, this yields a mixed AME state of optimal purity $1/2$, not subject to canonical graph-state constraints.

quant-ph↗

arXiv2026

Classifying the simplest Bell inequalities beyond qubits and their applications towards self-testing

Bell inequalities reveal the fundamentally nonlocal character of quantum mechanics. In this regard, one of the interesting problems is to explore all possible Bell inequalities that demonstrate a gap between local and nonlocal quantum behaviour. This is useful for the geometric characterisation of the set of nonlocal correlations achievable within quantum theory. Moreover, it provides a systematic way to construct Bell inequalities that are tailored to specific quantum information processing tasks. This characterisation is well understood in the simplest $(2,2,2)$ scenario, namely two parties performing two binary outcome measurements. However, beyond this setting, relatively few Bell inequalities are known, and the situation becomes particularly scarce in scenarios involving a greater number of outcomes. Here, we consider the $(2,2,3)$ scenario, or two parties performing two three-outcome measurements, and characterise all Bell inequalities that can arise from the simplest sum-of-squares decomposition and are maximally violated by the maximally entangled state of local dimension three. We then utilise them to self-test this state, along with a class of three-outcome measurements.

quant-ph↗

arXiv2025

Paradox-free classical non-causality and unambiguous non-locality without entanglement are equivalent

Closed timelike curves (CTCs) challenge our conception of causality by allowing information to loop back into its own past. Any consistent description of such scenarios must avoid time-travel paradoxes while respecting the no-new-physics principle, which requires that the set of operations available within any local spacetime region remain unchanged, irrespective of whether CTCs exist elsewhere. Within an information-theoretic framework, this leads to process functions: deterministic classical communication structures that remain logically consistent under arbitrary local operations, yet can exhibit correlations incompatible with any definite causal order - a phenomenon known as non-causality. In this work, we establish a correspondence between process functions and unambiguous complete product bases, i.e. product bases in which every local state belongs to a unique local basis. This equivalence implies that non-causality of process functions is exactly mirrored by quantum nonlocality without entanglement (QNLWE) - the impossibility of perfectly distinguishing separable states using local operations and causal classical communication - for such bases. Our results generalize previous special cases to arbitrary local dimensions and any number of parties, enable systematic constructions of non-causal process functions and unambiguous QNLWE bases, and implies, inter alia, that bipartite unambiguous QNLWE bases do not exist. Finally, this work reveals an unexpected connection between causal and non-signaling inequalities: every process function both maximally violates an associated causal inequality and yields a corresponding Bell inequality that admits no violation.

quant-ph↗

arXiv2025

Certifying Majorana Fermions with Elegant-Like Bell Inequalities and a New Self-Testing Equivalence

Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable through quantum strategies, is rarely accessible analytically. In this work, we introduce a general construction of Bell inequalities for which this bound can be computed exactly. Our framework generalizes both the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, yielding Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, our inequalities also enable the device-independent certification of Majorana fermions, understood as multiqubit realizations of Clifford algebra generators. Importantly, we identify an additional equivalence that must be incorporated into the definition of self-testing beyond invariance under local isometries and transposition. This equivalence arises from partial transposition applied to the shared state and to the measurements, which in specific cases leaves all observed correlations unchanged.

quant-ph↗

arXiv2025

Equivalence of Genuine Multipartite Entanglement and Nonlocality of Nearly Symmetric Multiqubit Pure States

Whether every pure genuinely multipartite entangled (GME) state necessarily exhibits genuine multipartite nonlocality (GMNL) remains an open question. By combining a recently proposed Bell inequality [I. Stachura \textit{et al.}, \href{https://iopscience.iop.org/article/10.1088/1367-2630/ad7753}{New J. Phys. \textbf{26}, 093029 (2024)}] with Hardy's paradox and the canonical decomposition of pure states, we analytically demonstrate that all highly symmetric, genuinely entangled multipartite qubit states exhibit genuine multipartite nonlocality, thereby supporting Gisin's conjecture in the multipartite setting. This result constitutes a step toward a general proof of the conjectured equivalence between GME and GMNL in quantum theory.

quant-ph↗

arXiv2025

Robust Self-Testing of Multiqudit Supersinglet Slater States via Constant Number of Binary Measurements

Self-testing is a powerful device-independent technique that enables one to deduce the forms of both the quantum state and the measurements involved in a physical experiment based solely on observed correlations. Although numerous schemes for self-testing multipartite entangled states have been proposed, they are typically difficult to implement experimentally, as their complexity increases significantly with the number of subsystems or the local dimension. In this work, we introduce the first self-testing scheme of a relevant class of multiqudit genuinely entangled states that exploits only a constant number of binary measurements per observer, which significantly reduces the experimental effort to implement the scheme. Specifically, it enables the self-testing of multipartite Slater (or supersinglet) states composed of $d$ qu\textit{d}its with odd $d$ using only four two-outcome measurements per observer. Moreover, we prove that our scheme is robust to noise and experimental imperfections. For systems of even local dimension $d$, we also provide an adapted version of the scheme that requires only $d$ binary measurements per observer.

quant-ph↗

arXiv2025

Entanglement witnesses for stabilizer states and subspaces beyond qubits

Genuine multipartite entanglement is arguably the most valuable form of entanglement in the multipartite case, with applications, for instance, in quantum metrology. In order to detect that form of entanglement in multipartite quantum states, one typically uses entanglement witnesses. The aim of this paper is to generalize the results of [G. T\'oth and O. G\"uhne, Phys. Rev. A \textbf{72}, 022340 (2005)] in order to provide a construction of witnesses of genuine multipartite entanglement tailored to entangled subspaces originating from the \textit{multi-qudit} stabilizer formalism -- a framework well known for its role in quantum error correction, which also provides a very convenient description of a broad class of entangled multipartite states (both pure and mixed). Our construction includes graph states of arbitrary local dimension. We then show that in certain situations, the obtained witnesses detecting genuine multipartite entanglement in quantum systems of higher local dimension are superior in terms of noise robustness to those derived for multiqubit states.

quant-ph↗

arXiv2025

Frustration graph formalism for qudit observables

The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian unitary operators whose eigenvalues are d'th roots of unity. We additionally assume that these observables mutually commute up to a scalar factor being one of the d'th roots of unity. By representing commutation relations of these observables via a frustration graph, we show that for such a group, there exists a single unitary transforming them into a tensor product of generalized Pauli matrices and some ancillary mutually commuting operators. Building on this result, we derive upper bounds on the sum of the squares of the absolute values and the sum of the expected values of the observables forming a group. We finally utilize these bounds to compute the generalized geometric measure of entanglement for qudit stabilizer subspaces.

quant-ph↗

arXiv2025

Gap between quantum theory based on real and complex numbers is arbitrarily large

Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be explained by Real Quantum Theory (RQT), a quantum theory with real Hilbert spaces instead of complex ones, when three parties are involved in a quantum network with non-trivial locality constraints. In this work, we study a scenario with $N+1$ parties sharing quantum systems in a star network. Here, we construct a "conditional" multipartite Bell inequality that exhibits a gap between RQT and CQT, which linearly increases with $N$ and is thus arbitrarily large in the asymptotic limit. This implies, that, as the number of parties grows, Hilbert space formalism based on real numbers becomes exceedingly worse at describing complex networks of quantum systems. Furthermore, we also compute the tolerance of this gap to experimental errors.

quant-ph↗

arXiv2025

Local unambiguous unidentifiability, entanglement generation, and Hilbert space splitting

We consider collections of mixed states supported on mutually orthogonal subspaces whose rank add up to the total dimension of the underlying Hilbert space. We then ask whether it is possible to find such collections in which no state from the set can be unambiguously identified by local operations and classical communication (LOCC) with non-zero success probability. We show the necessary and sufficient condition for such a property to exist is that the states must be supported in entangled subspaces. In fact, the existence of such a set guarantees the existence of a type of entangling projective measurement other than rank one measurements and vice versa. This projective measurement can create entanglement from any product state picked from the same Hilbert space on which the measurement is applied. Here the form of the product state is not characterized. Ultimately, these sets or the measurements are associated with the splitting of a composite Hilbert space, i.e., the Hilbert space can be written as a direct sum of several entangled subspaces. We then characterize present sets (measurements) in terms of dimensional constraints, maximum-minimum cardinalities (outcomes), etc. The maximum cardinalities of the sets constitute a class of state discrimination tasks where several stronger classes of measurements (like separable measurements, etc.) do not provide any advantage over LOCC. Finally, we discuss genuine local unambiguous unidentifiability and generation of genuine entanglement from completely product states.

quant-ph↗

arXiv2024

All pure multipartite entangled states of qubits can be self-tested up to complex conjugation

Self-testing refers to the certification of quantum states and measurements based entirely on the correlations exhibited by measurements on separate subsystems. In the bipartite case, self-testing of states has been completely characterized, up to local isometries, as there exist protocols that self-test arbitrary pure states of any local dimension. Much less is known in the multipartite case, where an important difference with respect to the bipartite case appears: there exist multipartite states that are not equivalent, up to local isometries, to their complex conjugate. Thus, any self-testing characterization must in general be complete up to not only local unitaries, but also complex conjugation. Under these premises, in this work, we give a complete characterization of self-testing in the multipartite qubit case.

quant-ph↗

arXiv2024

Certifying classes of $d$-outcome measurements with quantum steering

Device-independent (DI) certification schemes are based on minimal assumptions about the quantum system under study, which makes the most desirable among certification schemes. However, they are often the most challenging to implement. In order to reduce the implementation cost one can consider semi-DI (SDI) schemes such as those based on quantum steering. Here we provide a construction of a family of steering inequalities which are tailored to large classes of d-outcomes projective measurements being a certain linear combination of the Heisenberg-Weyl operators on the untrusted side and a fixed set of known measurements on the trusted side. We then prove that the maximal quantum violation of those inequalities can be used for certification of those measurements and the maximally entangled state of two qudits. Importantly, in our self-testing proof, we do not assume the shared state to be pure, nor do we assume the measurements to be projective. Before concluding, we also show how robust to noise our self-testing statement is. We believe that our construction broadens the scope of SDI certification, paving the way for more general but still less costly quantum certification protocols.

quant-ph↗

arXiv2024

Single Bell inequality to detect genuine nonlocality in three-qubit genuinely entangled states

It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in [F. J. Curchod, M. L. Almeida, and A. Acin, New J. Phys. 21, 023016 (2019) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver tighter Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.

quant-ph↗