arXiv subjects

Arturo Konderak

Publications and source records attributed to Arturo Konderak.

12 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

Decoherence-free algebras in quantum dynamics

In this Article we analyze the algebraic properties of the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. In particular, a natural product (Choi-Effros product) can be defined in the asymptotic regime. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. Interestingly, this space is both a C*-algebra with respect to the composition product, and a B*-algebra with respect to the Choi-Effros product. Moreover, such space admits a direct-sum decomposition revealing a clear relationship with the attractor subspace of the dynamics. In particular, the equality between the attractor subspace and the Choi-Effros decoherence-free algebra is a necessary and sufficient condition for a faithful dynamics. Finally, we show how all the findings do not rely on complete positivity but on the much weaker Schwarz property.

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↗

arXiv2025

Systematic construction of ROCN Bell-inequalities

Self-testing constitutes one of the most powerful forms of device certification, enabling a complete and device-independent characterization of a quantum apparatus solely from the observed correlations. In recent work by the authors [23], a general framework was introduced for constructing Bell inequalities that self-test entire families of Clifford generators. In this manuscript, we develop an alternative and complementary self-testing criterion based on symmetric spanning sets. This formulation provides an explicit and constructive route to designing self-testing Bell inequalities in arbitrary dimensions.

quant-ph↗

arXiv2025

Attractor Subspace and Decoherence-Free Algebra of Quantum Dynamics

In this review we discuss some results on the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. Both the spectral and algebraic approaches to this topic are addressed, with particular emphasis on their relationship. The analysis is conducted in both the discrete-time and the continuous-time Markovian settings. In the final part of the work, some issues emerging in the infinite-dimensional case are also discussed. In particular, we provide an example of a Markovian evolution whose decoherence-free algebra is a type III von Neumann algebra.

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

Asymptotic dynamics in the Heisenberg picture: attractor subspace and Choi-Effros product

We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor subspaces in the Schrödinger and Heisenberg pictures and, in particular, the connection between their algebraic structures. An unfolding theorem of the asymptotics, as well as the fine structure of the recently introduced Choi-Effros decoherence-free algebra, are also discussed. Finally, we show how to extend all the results to the class of Schwarz maps.

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↗

arXiv2023

Asymptotic Dynamics of Open Quantum Systems and Modular Theory

In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization for its unitarity. Interestingly, this is not always guaranteed due to the presence of permutations in the structure of the asymptotic map. Then, we show the connection between the asymptotic map and the modular theory by Tomita and Takesaki.

quant-ph↗

arXiv2023

Asymptotics of quantum channels

We discuss several aspects concerning the asymptotic dynamics of dicrete-time semigroups associated with a quantum channel. By using an explicit expression of the asymptotic map, which describes the action of the quantum channel on its attractor manifold, we investigate the role of permutations in the asymptotic dynamics. We show that, in general, they make the asymptotic evolution non-unitary, and they are related to the divisibility of the quantum channel. Also, we derive several results about the asymptotics of faithful and non-faithful channels, and we establish a constructive unfolding theorem for the asymptotic dynamics.

quant-ph↗

arXiv2023

Groupoid and algebra of the infinite quantum spin chain

It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with finite density. This forces us to introduce different types of algebras, more general than the ones we usually encounter in a standard course of quantum mechanics. We show how these algebras naturally arise in the Schwinger description of the quantum mechanics of an infinite spin chain. In particular, we use the machinery of Dirac-Feynman-Schwinger (DFS) states developed in recent works to introduce a dynamics based on the modular theory by Tomita-Takesaki, and consequently we apply this approach to describe the Ising model.

quant-ph↗

arXiv2021

Entropy of quantum states

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to its possible decompositions into pure states, we give a purely algebraic definition of entropy for states of an algebra of observables, thus solving the above ambiguity. The entropy so defined satisfies all the desirable thermodynamic properties, and reduces to the von Neumann entropy in the quantum mechanical case. Moreover, it can be shown to be equal to the von Neumann entropy of the unique representative density matrix belonging to the operator algebra of a multiplicity-free Hilbert-space representation.

quant-ph↗