arXiv subjects

Tamas Vertesi

Publications and source records attributed to Tamas Vertesi.

At least 19 recordsLinked to original sources

arXiv2026

Permutation asymmetry unlocks emergent advantage in randomized Bell tests

All maximally entangled two-qubit states violate local realism with the same probability under uniformly random projective measurements, yet they need not behave identically in randomized Bell tests. We show that when measurement settings are exchanged between the parties in sequential Bell experiments, permutation symmetry of the shared state determines the statistical relation between the two realizations. Permutationally invariant states yield identical nonlocality outcomes in both experiments, whereas asymmetric states can violate local realism in one realization but not in the other. This distinction leads to two operational consequences. First, it enables the detection of correlations between the measurement choices of Alice and Bob through the joint violation statistics. Second, in Bell tests with finite measurement pools, asymmetric maximally entangled states can significantly increase the probability of observing nonlocality without requiring additional resources. Our results identify permutation asymmetry as a useful feature in randomized Bell experiments and highlight a new role of symmetry in quantum nonlocality.

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arXiv2022

Optimal tests of genuine multipartite nonlocality

We propose an optimal numerical test for genuine multipartite nonlocality based on linear programming. In particular, we consider two non-equivalent models of local hidden variables, namely the Svetlichny and the no-signaling bilocal model. While our knowledge concerning these models is well established for Bell scenarios involving two measurement settings per party, the general case based on an arbitrary number of settings is a considerably more challenging task and very little work has been done in this field. In this paper, we applied such general tests to detect and characterize genuine $n$-way nonlocal correlations for various states of three qubits and qutrits. As a measure of nonlocality, we use the probability of violation of local realism under randomly sampled observables, and the strength of nonlocality, described by the resistance to white noise admixture. In particular, we analyze to what extent the Bell scenario involving two measurement settings can be used to determine genuine $n$-way non-local correlations generated for more general models. In addition, we propose a simple procedure to detect genuine multipartite nonlocality for randomly chosen settings with up to 100% efficiency.

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arXiv2019

$k$-uniform mixed states

We investigate the maximum purity that can be achieved by k-uniform mixed states of N parties. Such N-party states have the property that all their k-party reduced states are maximally mixed. A scheme to construct explicitly k-uniform states using a set of specific N-qubit Pauli matrices is proposed. We provide several different examples of such states and demonstrate that in some cases the state corresponds to a particular orthogonal array. The obtained states, despite being mixed, reveal strong non-classical properties such as genuine multipartite entanglement or violation of Bell inequalities.

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arXiv2019

Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios

In this work we investigate the probability of violation of local realism under random measurements in parallel with the strength of these violations as described by resistance to white noise admixture. We address multisetting Bell scenarios involving up to 7 qubits. As a result, in the first part of this manuscript we report statistical distributions of a quantity reciprocal to the critical visibility for various multipartite quantum states subjected to random measurements. The statistical relevance of different classes of multipartite tight Bell inequalities violated with random measurements is investigated. We also introduce the concept of typicality of quantum correlations for pure states as the probability to generate a nonlocal behaviour with both random state and measurement. Although this typicality is slightly above 5.3\% for the CHSH scenario, for a modest increase in the number of involved qubits it quickly surpasses 99.99\%.

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arXiv2019

Disproving hidden variable models with spin magnitude conservation

The squares of the three components of the spin-s operators sum up to $s(s+1)$. However, a similar relation is rarely satisfied by the set of possible spin projections onto mutually orthogonal directions. This has fundamental consequences if one tries to construct a hidden variable (HV) theory describing measurements of spin projections. We propose a test of local HV-models in which spin magnitudes are conserved. These additional constraints imply that the corresponding inequalities are violated within quantum theory by larger classes of correlations than in the case of standard Bell inequalities. We conclude that in any HV-theory pertaining to measurements on a spin one can find situations in which either HV-assignments do not represent a physical reality of a spin vector, but rather provide a deterministic algorithm for prediction of the measurement outcomes, or HV-assignments represent a physical reality, but the spin cannot be considered as a vector of fixed length.

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arXiv2018

Closing the detection loophole in multipartite Bell experiments with a limited number of efficient detectors

The problem of closing the detection loophole in Bell tests is investigated in the presence of a limited number of efficient detectors using emblematic multipartite quantum states. To this end, a family of multipartite Bell inequalities is introduced basing on local projective measurements conducted by $N-k$ parties and applying a $k$-party Bell inequality on the remaining parties. Surprisingly, we find that most of the studied pure multipartite states involving e.g. cluster states, the Dicke states, and the Greenberger-Horne-Zeilinger states can violate our inequalities with only the use of two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies. We believe that our inequalities are useful in Bell experiments and device-independent applications if only a small number of highly efficient detectors are in our disposal.

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arXiv2018

Bond dimension witnesses and the structure of homogeneous matrix product states

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via site-independent tensors and a boundary condition. Exploiting a connection with the theory of matrix algebras, we derive two structural properties shared by all hMPS, namely: a) there exist local operators which annihilate all hMPS of a given bond dimension; and b) there exist local operators which, when applied over any hMPS of a given bond dimension, decouple (cut) the particles where they act from the spin chain while at the same time join (glue) the two loose ends back again into a hMPS. Armed with these tools, we show how to systematically derive `bond dimension witnesses', or 2-local operators whose expectation value allows us to lower bound the bond dimension of the underlying hMPS. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS to: a) derive some theoretical limitations on the use of hMPS and hPEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.

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arXiv2017

Family of Bell inequalities violated by higher-dimensional bound entangled states

We construct ($d\times d$)-dimensional bound entangled states, which violate, for any $d>2$, a bipartite Bell inequality introduced in this paper. We conjecture that the proposed class of Bell inequalities acts as a dimension witness for bound entangled states: For any $d>2$ there exists a Bell inequality from this class that can be violated with bound entangled states only if their Hilbert space dimension is at least $d\times d$. Numerics supports this conjecture up to $d=8$.

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arXiv2017

Multipartite nonlocality and random measurements

We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.

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arXiv2017

Convex separation from convex optimization for large-scale problems

We present a scheme, based on Gilbert's algorithm for quadratic minimization [SIAM J. Contrl., vol. 4, pp. 61-80, 1966], to prove separation between a point and an arbitrary convex set $S\subset\mathbb{R}^{n}$ via calls to an oracle able to perform linear optimizations over $S$. Compared to other methods, our scheme has almost negligible memory requirements and the number of calls to the optimization oracle does not depend on the dimensionality $n$ of the underlying space. We study the speed of convergence of the scheme under different promises on the shape of the set $S$ and/or the location of the point, validating the accuracy of our theoretical bounds with numerical examples. Finally, we present some applications of the scheme in quantum information theory. There we find that our algorithm out-performs existing linear programming methods for certain large scale problems, allowing us to certify nonlocality in bipartite scenarios with upto $42$ measurement settings. We apply the algorithm to upper bound the visibility of two-qubit Werner states, hence improving known lower bounds on Grothendieck's constant $K_G(3)$. Similarly, we compute new upper bounds on the visibility of GHZ states and on the steerability limit of Werner states for a fixed number of measurement settings.

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arXiv2015

Highly noise resistant multipartite quantum correlations

We analyze robustness of correlations of the $N$-qubit GHZ and Dicke states against white noise admixture. For sufficiently large $N$, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for $N=9$ for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are partially product. As a by-product, we obtain a simple three-setting Bell inequality which is violated by any pure entangled state.

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arXiv2015

Bell inequalities violated using detectors of low efficiency

We define a family of binary outcome $n$-party $m\leq n$ settings per party Bell inequalities whose members require the least detection efficiency for their violation among all known inequalities of the same type. This gives upper bounds for the minimum value of the critical efficiency --- below which no violation is possible --- achievable for such inequalities. For $m=2$, our family reduces to the one given by Larsson and Semitecolos in 2001. For $m>2$, a gap remains between these bounds and the best lower bounds. The violating state near the threshold efficiency always approaches a product state of $n$ qubits.

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arXiv2015

Characterizing finite-dimensional quantum behavior

We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device independent and semi-device independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive new dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes.

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arXiv2015

Closing the detection loophole in tripartite Bell tests using the W state

We study the problem of closing the detection loophole in three-qubit Bell tests, the experimentally most relevant case beyond the usual bipartite scenario, and show that the minimal detection efficiencies required can be considerably lowered compared to the two-qubit case. The lowest reported detection efficiency thresholds for two and three qubits so far are $\sim66.7\%$ and $60\%$, respectively. Using the three-qubit W state and a 3-setting Bell inequality, we beat these thresholds and with an 8-setting Bell inequality we reach $50.13\%$. We also investigate generic three-qubit states which allow us to attain a detection efficiency of $50\%$ in a 4-setting Bell test. We conjecture that the limit of $50\%$ is unbeatable using three-qubit states and any number of measurements.

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arXiv2014

Bounding the set of finite dimensional quantum correlations

We describe a simple method to derive high performance semidefinite programming relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in bipartite and tripartite Bell scenarios where the dimension of a subset of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepare-and-measure dimension witnesses introduced in [Phys. Rev. Lett. 105, 230501 (2010)]. Finally, we propose a new dimension witness that can distinguish between classical, real and complex two-level systems.

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arXiv2014

Device-independent tomography of multipartite quantum states

In the usual tomography of multipartite entangled quantum states one assumes that the measurement devices used in the laboratory are under perfect control of the experimenter. In this paper, using the so-called SWAP concept introduced recently, we show how one can remove this assumption in realistic experimental conditions and nevertheless be able to characterize the produced multipartite state based only on observed statistics. Such a black box tomography of quantum states is termed self-testing. As a function of the magnitude of the Bell violation, we are able to self-test emblematic multipartite quantum states such as the three-qubit W state, the three- and four-qubit Greenberger-Horne-Zeilinger states, and the four-qubit linear cluster state.

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arXiv2014

Certifying nonlocality from separable marginals

Imagine three parties, Alice, Bob, and Charlie, who share a state of three qubits such that all two-party reduced states A-B,A-C, and B-C are separable. Suppose that they have information only about these marginals but not about the global state. According to recent results, there exists an example for a set of three separable two-party reduced states that is only compatible with an entangled global state. In this paper, we show a stronger result, by exhibiting separable two-party reduced states A-B, A-C, and B-C, such that any global state compatible with these marginals is nonlocal. Hence, we obtain that nonlocality of multipartite states can be certified from information only about separable marginals.

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arXiv2014

Closed sets of correlations: answers from the zoo

We investigate the conditions under which a set of multipartite nonlocal correlations can describe the distributions achievable by distant parties conducting experiments in a consistent universe. Several questions are posed, such as: are all such sets "nested", i.e., contained into one another? Are they discrete or do they form a continuum? How many of them are supraquantum? Are there non-trivial polytopes among them? We answer some of these questions or relate them with established conjectures in complexity theory by introducing a "zoo" of physically consistent sets which can be characterized efficiently via either linear or semidefinite programming. As a bonus, we use the zoo to derive, for the first time, concrete impossibility results in nonlocality distillation.

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