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In a Bell test involving three parties, one may find a curious situation where the nonlocality in two bipartite subsystems forces the remaining bipartite subsystem to exhibit nonlocality. Post-quantum examples for this phenomenon, dubbed nonlocality transitivity, have been found in 2011. However, the question of whether nonlocality transitivity occurs within quantum theory has remained unresolved -- until now. Here, we provide the first affirmative answer to this question at the level of quantum states. Leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system forces the remaining bipartite state to be nonlocal. En route to showing this, we prove that multiple copies of the $W$-state marginals uniquely determine the global compatible state. Furthermore, in contrast to Bell-nonlocality, we show that quantum steering already exhibits transitivity in a three-qubit setting, thus revealing another significant distinction between Bell-nonlocality and steering. We also discuss connections between the problem of nonlocality transitivity and the largely overlooked polygamous nature of nonlocality., Comment: 8+ pages, 1 figure; this is Ref. [86] of arXiv:2202.03523

Entanglement is an essential resource for various quantum-information tasks. When a target system shares entanglement with another memory system and is stored reliably, one can use entanglement at a later time -- this is quantum memory. In practice, entanglement can be exceedingly fragile during a system's evolution. In particular, no entanglement can survive when a so-called entanglement-breaking channel acts on the target system. Are entanglement-breaking channels really useless for maintaining entanglement? As a single channel, this is certainly the case; it cannot be useful for quantum memory. However, in this work, we show that putting together two entanglement-breaking channels in a broadcasting scenario can activate their ability to maintain entanglement -- the channel's quantum memory resource can be super-activated., Comment: 4+3 pages, 2 figures

Entanglement is at the heart of quantum theory and is responsible for various quantum-enabling technologies. In practice, during its preparation, storage, and distribution to the intended recipients, this valuable quantum resource may suffer from noisy interactions that reduce its usefulness for the desired information-processing tasks. Conventional schemes of entanglement distillation aim to alleviate this problem by performing collective operations on multiple copies of these decohered states and sacrificing some of them to recover Bell pairs. However, for this scheme to work, the states to be distilled should already contain a large enough fraction of maximally entangled states before these collective operations. Not all entangled quantum states meet this premise. Here, by using the paradigmatic family of two-qutrit Werner states as an exemplifying example, we experimentally demonstrate how one may use single-copy local filtering operations to meet this requirement and to recover the quantumness hidden in these higher-dimensional states. Among others, our results provide the first proof-of-principle experimental certification of the Bell-nonlocal properties of these intriguing entangled states, the activation of their usefulness for quantum teleportation, dense coding, and an enhancement of their quantum steerability, and hence usefulness for certain discrimination tasks. Our theoretically established lower bounds on the steering robustness of these states, when they admit a symmetric quasiextension or a bosonic symmetric extension, and when they show hidden dense-codability may also be of independent interest., Comment: 16 pages, 15 figures

Probing the neutral gas distribution at the edge of magnetic confinement fusion devices is critical for divertor physics studies. In the TCV tokamak, a set of ASDEX-type hot ionization pressure gauges (APGs) has been installed for fast, in-situ measurements of the neutral pressure distribution in the TCV chamber. The APGs have been calibrated against baratron pressure gauges (BGs) for pressures ranging from less than 1 mPa to several hundred mPa. A correction to account for the residual pressure in the pumped torus is proposed to improve the measurement accuracy. APG measurements in a series of plasma discharges with varied density ramp rates are analyzed, and are compared with the pressure measurements of the existing BGs. APG measurements feature significantly higher time resolution and faster time response than the BGs, and extend the measurement range to lower pressures. APGs systematically measure higher neutral pressures than the BGs connected to the same TCV port, likely due to the BG time delay and slow time response and nonuniform neutral distribution in gauge ports during the discharge. The initial APG operations in TCV have been proven successful, which validates the APG as an adequate pressure measurement technique for the upcoming TCV divertor upgrades.

As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local-hidden variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A. 98, 062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, a special case of which is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided., Comment: 9 pages, 6 figures, 3 tables; Comments are welcome!

De novo molecule generation can suffer from data inefficiency; requiring large amounts of training data or many sampled data points to conduct objective optimization. The latter is a particular disadvantage when combining deep generative models with computationally expensive molecule scoring functions (a.k.a. oracles) commonly used in computer-aided drug design. Recent works have therefore focused on methods to improve sample efficiency in the context of de novo molecule drug design, or to benchmark it. In this work, we discuss and adapt a recent sample efficiency benchmark to better reflect realistic goals also with respect to the quality of chemistry generated, which must always be considered in the context of small-molecule drug design; we then re-evaluate all benchmarked generative models. We find that accounting for molecular weight and LogP with respect to the training data, and the diversity of chemistry proposed, re-orders the ranking of generative models. In addition, we benchmark a recently proposed method to improve sample efficiency (Augmented Hill-Climb) and found it ranked top when considering both the sample efficiency and chemistry of molecules generated. Continual improvements in sample efficiency and chemical desirability enable more routine integration of computationally expensive scoring functions on a more realistic timescale., Comment: Submission to ELLIS ML4Molecules Workshop 2022

In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing $k$ zero probabilities, we provide a $(5-k)$-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set $\mathcal{M}$ of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of $\mathcal{M}$ in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states., Comment: v3: 16+14 pages, 9 figures, 6 tables; v2: 15+12 pages, 9 figures, 5 tables, robust self-testing results and references added; v1: 12+11 pages, 3 figures, 5 tables

We examine the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). Interestingly, even if we employ only two-setting Bell inequalities, we find a significant chance of obtaining a Bell violation if the two parties are individually allowed to measure a sufficient number of MUBs. In particular, for the case of maximally entangled qutrits and ququarts, our numerical estimates indicate that we can obtain near-guaranteed Bell violation by considering only such Bell inequalities. The case of maximally entangled ququints is similar, albeit the chance of ending up with a successful trial decreases somewhat to approximately $99.84\%$. Upon a closer inspection, we find that even all these no-violation instances violate some more-setting Bell inequalities. These results suggest that the experimental tests of Bell nonlocality for these higher-dimensional entangled states remain viable even if the two parties do not share a common reference frame., Comment: 10+1 pages, 9 figures, 6 tables. v2 is essentially the same as the published version

One of the goals of science is to understand the relation between a whole and its parts, as exemplified by the problem of certifying the entanglement of a system from the knowledge of its reduced states. Here, we focus on a different but related question: can a collection of marginal information reveal new marginal information? We answer this affirmatively and show that (non-) entangled marginal states may exhibit (meta)transitivity of entanglement, i.e., implying that a different target marginal must be entangled. By showing that the global $n$-qubit state compatible with certain two-qubit marginals in a tree form is unique, we prove that transitivity exists for a system involving an arbitrarily large number of qubits. We also completely characterize -- in the sense of providing both the necessary and sufficient conditions -- when (meta)transitivity can occur in a tripartite scenario when the two-qudit marginals given are either the Werner states or the isotropic states. Our numerical results suggest that in the tripartite scenario, entanglement transitivity is generic among the marginals derived from pure states., Comment: 8+10 pages, 9 figures, 2 tables. Virtually the same as the published version

We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility induces a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem -- which implicitly involves some notion of incompatibility -- for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems., Comment: 14+16 pages and 3 figures. New results added and largely rewritten. Accepted for publication in Quantum

Ideal quantum teleportation transfers an unknown quantum state intact from one party Alice to the other Bob via the use of a maximally entangled state and the communication of classical information. If Alice and Bob do not share entanglement, the maximal average fidelity between the state to be teleported and the state received, according to a classical measure-and-prepare scheme, is upper bounded by a function $f_{\mathrm{c}}$ that is inversely proportional to the Hilbert space dimension. In fact, even if they share entanglement, the so-called teleportation fidelity may still be less than the classical threshold $f_{\mathrm{c}}$. For two-qubit entangled states, conditioned on a successful local filtering, the teleportation fidelity can always be activated, i.e., boosted beyond $f_{\mathrm{c}}$. Here, for all dimensions larger than two, we show that the teleportation power hidden in a subset of entangled two-qudit Werner states can also be activated. In addition, we show that an entire family of two-qudit rank-deficient states violates the reduction criterion of separability, and thus their teleportation power is either above the classical threshold or can be activated. Using hybrid entanglement prepared in photon pairs, we also provide the first proof-of-principle experimental demonstration of the activation of teleportation power hidden in this latter family of qubit states. The connection between the possibility of activating hidden teleportation power with the closely-related problem of entanglement distillation is discussed., Comment: 6 + 12 pages, 13 figures, 4 tables. v3 virtually the same as the published version

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.