arXiv subjects

L. Aolita

Publications and source records attributed to L. Aolita.

At least 19 recordsLinked to original sources

arXiv2026

A quantum-inspired multi-level tensor-train monolithic space-time method for nonlinear PDEs

We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed high-dimensional simulations, the literature contains few systematic comparisons with classical time-stepping methods, limited error convergence analyses, and little quantitative assessment of the impact of TT rounding on numerical accuracy. Likewise, existing studies fail to demonstrate performance across a diverse set of PDEs and parameter ranges. In practice, monolithic Newton iterations may stagnate or fail to converge in strongly nonlinear, stiff, or advection-dominated regimes, where poor initial guesses and severely ill-conditioned space-time Jacobians hinder robust convergence. We overcome this limitation by introducing a coarse-to-fine multilevel strategy fully embedded within the TT format. Each level refines both spatial and temporal resolutions while transferring the TT solution through low-rank prolongation operators, providing robust initializations for successive Newton solves. Residuals, Jacobians, and transfer operators are represented directly in TT and solved with the adaptive-rank DMRG algorithm. Numerical experiments for a selection of nonlinear PDEs including Fisher-KPP, viscous Burgers, sine-Gordon, and KdV cover diffusive, convective, and dispersive dynamics, demonstrating that the multilevel TT approach consistently converges where single-level space-time Newton iterations fail. In dynamic, advection-dominated (nonlinear) scenarios, multilevel TT surpasses single-level TT, achieving high accuracy with significantly reduced computational cost, specifically when high-fidelity numerical simulation is required.

math.NA↗

arXiv2021

Exposure of subtle multipartite quantum nonlocality

The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect whereby local operations could create steering seemingly from scratch. Nevertheless, neither in steering nor in Bell nonlocality has this effect been experimentally confirmed. Operational consistency is reestablished by presenting a suitable redefinition: there is a subtle form of steering already present at the start, and it is only exposed -- as opposed to created -- by the local operations. We devise protocols that, remarkably, are able to reveal, in seemingly unsteerable systems, not only steering, but also Bell nonlocality. Moreover, we find concrete cases where entanglement certification does not coincide with steering. A causal analysis reveals the crux of the issue to lie in hidden signaling. Finally, we implement one of the protocols with three photonic qubits deterministically, providing the experimental demonstration of both exposure and super-exposure of quantum nonlocality.

quant-ph↗

arXiv2020

Boson-Sampling in the light of sample complexity

Boson-Sampling is a classically computationally hard problem that can - in principle - be efficiently solved with quantum linear optical networks. Very recently, a rush of experimental activity has ignited with the aim of developing such devices as feasible instances of quantum simulators. Even approximate Boson-Sampling is believed to be hard with high probability if the unitary describing the optical network is drawn from the Haar measure. In this work we show that in this setup, with probability exponentially close to one in the number of bosons, no symmetric algorithm can distinguish the Boson-Sampling distribution from the uniform one from fewer than exponentially many samples. This means that the two distributions are operationally indistinguishable without detailed a priori knowledge. We carefully discuss the prospects of efficiently using knowledge about the implemented unitary for devising non-symmetric algorithms that could potentially improve upon this. We conclude that due to the very fact that Boson-Sampling is believed to be hard, efficient classical certification of Boson-Sampling devices seems to be out of reach.

quant-ph↗

arXiv2020

Distillation of quantum steering

We show -- both theoretically and experimentally -- that Einstein-Podolsky-Rosen steering can be distilled. We present a distillation protocol that outputs a perfectly correlated system -- the singlet assemblage -- in the asymptotic infinite-copy limit, even for inputs that are arbitrarily close to being unsteerable. As figures of merit for the protocol's performance, we introduce the assemblage fidelity and the singlet-assemblage fraction. These are potentially interesting quantities on their own beyond the current scope. Remarkably, the protocol works well also in the non-asymptotic regime of few copies, in the sense of increasing the singlet-assemblage fraction. We demonstrate the efficacy of the protocol using a hyperentangled photon pair encoding two copies of a two-qubit state. This represents to our knowledge the first observation of deterministic steering concentration. Our findings are not only fundamentally important but may also be useful for semi device-independent protocols in noisy quantum networks.

quant-ph↗

arXiv2018

Fidelity witnesses for fermionic quantum simulations

The experimental interest and developments in quantum spin-1/2-chains has increased uninterruptedly over the last decade. In many instances, the target quantum simulation belongs to the broader class of non-interacting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally-friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.

quant-ph↗

arXiv2018

Quantum steering beyond instrumental causal networks

We theoretically predict, and experimentally verify with entangled photons, that outcome communication is not enough for hidden-state models to reproduce quantum steering. Hidden-state models with outcome communication correspond, in turn, to the well-known instrumental processes of causal inference but in the 1-sided device-independent (1S DI) scenario of one black-box measurement device and one well-characterised quantum apparatus. We introduce 1S-DI instrumental inequalities to test against these models, with the appealing feature of detecting entanglement even when communication of the black box's measurement outcome is allowed. We find that, remarkably, these inequalities can also be violated solely with steering, i.e. without outcome communication. In fact, an efficiently-computable formal quantifier -- the robustness of non-instrumentality -- naturally arises; and we prove that steering alone is enough to maximize it. Our findings imply that quantum theory admits a stronger form of steering than known until now, with fundamental as well as practical potential implications.

quant-ph↗

arXiv2017

A formalism for steering with local quantum measurements

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.

quant-ph↗

arXiv2016

Necessary and sufficient conditions for multipartite Bell violations with only one trusted device

We study multipartite Bell nonlocality in a framework native of multipartite Einstein-Podolsky-Rosen (EPR) steering scenarios with a single trusted measurement device. We derive a closed-form necessary and sufficient criterion for systems composed of a qubit and N-1 untrusted black-box measurement devices to violate -- under general dichotomic measurements on the qubit -- a generic Bell inequality from a broad family of linear inequalities with arbitrarily many outputs for the N-1 untrusted devices and inputs for all N parties. The optimal quantum measurements for maximal violation are also obtained. For two users, and two inputs and two outputs per user, our criterion becomes necessary and sufficient for Bell nonlocality. Furthermore, in that setting, its form generalizes recently obtained steering inequalities, which allows us to provide useful feedback from nonlocality to the detection of steering. Our findings constitute a practical tool for the study of the interplay between EPR steering and Bell nonlocality, with potential applications in multipartite information processing.

quant-ph↗

arXiv2015

Reliable quantum certification for photonic quantum technologies

A major roadblock for large-scale photonic quantum technologies is the lack of practical reliable certification tools. We introduce an experimentally friendly - yet mathematically rigorous - certification test for experimental preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states generated by linear-optical circuits with n-boson Fock-basis states as inputs, and states of these two classes subsequently post-selected with local measurements on ancillary modes. The protocol is efficient in m and the inverse post-selection success probability for all Gaussian states and all mentioned non-Gaussian states with constant n. We follow the mindset of an untrusted prover, who prepares the state, and a skeptic certifier, with classical computing and single-mode homodyne-detection capabilities only. No assumptions are made on the type of noise or capabilities of the prover. Our technique exploits an extremality-based fidelity bound whose estimation relies on non-Gaussian state nullifiers, which we introduce on the way as a byproduct result. The certification of many-mode photonic networks, as those used for photonic quantum simulations, boson samplers, and quantum metrology, is now within reach.

quant-ph↗

arXiv2014

Linear-optical simulation of the cooling of a cluster-state Hamiltonian system

A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond to cooling the system. We perform an experimental quantum simulation of such cooling process with entangled photons. We prepare three-qubit thermal cluster states exploiting the equivalence between local dephasing and thermalisation for these states. This allows us to tune the system's temperature by changing the dephasing strength. We monitor the entanglement as the system cools down and observe the transitions from separability to bound entanglement, and then to free entanglement. We also analyze the performance of the system for measurement-based single-qubit state preparation. These studies constitute a basic characterisation of experimental cluster-state computation under imperfect conditions.

quant-ph↗

arXiv2013

Photonic polarization gears for ultra-sensitive angular measurements

Quantum metrology bears a great promise in enhancing measurement precision, but is unlikely to become practical in the near future. Its concepts can nevertheless inspire classical or hybrid methods of immediate value. Here, we demonstrate NOON-like photonic states of m quanta of angular momentum up to m=100, in a setup that acts as a "photonic gear", converting, for each photon, a mechanical rotation of an angle θ into an amplified rotation of the optical polarization by mθ, corresponding to a "super-resolving" Malus' law. We show that this effect leads to single-photon angular measurements with the same precision of polarization-only quantum strategies with m photons, but robust to photon losses. Moreover, we combine the gear effect with the quantum enhancement due to entanglement, thus exploiting the advantages of both approaches. The high "gear ratio" m boosts the current state-of-the-art of optical non-contact angular measurements by almost two orders of magnitude.

quant-ph↗

arXiv2011

Quantum locking of classical correlations and quantum discord of classical-quantum states

A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to approach unconditional security, then the key and the message must have comparable sizes. But if Alice prepares a quantum state, the size of the key can be comparatively negligible. This effect is called quantum locking. Entanglement does not play a role in this quantum advantage. We show that, in this scenario, the quantum discord quantifies the advantage of the quantum protocol over the corresponding classical one for any classical-quantum state.

quant-ph↗

arXiv2011

Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms of entanglement consumption in an extended quantum state merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.

quant-ph↗

arXiv2011

Noisy entanglement evolution for graph states

A general method for the study of the entanglement evolution of graph states under the action of Pauli was recently proposed in [Cavalcanti, et al., Phys. Rev. Lett. 103, 030502 (2009)]. This method is based on lower and upper bounds on the entanglement of the entire state as a function only of the state of a considerably-smaller subsystem, which undergoes an effective noise process. This provides a huge simplification on the size of the matrices involved in the calculation of entanglement in these systems. In the present paper we elaborate on this method in details and generalize it to other natural situations not described by Pauli maps. Specifically, for Pauli maps we introduce an explicit formula for the characterization of the resulting effective noise. Beyond Pauli maps, we show that the same ideas can be applied to the case of thermal reservoirs at arbitrary temperature. In the latter case, we discuss how to optimize the bounds as a function of the noise strength. We illustrate our ideas with explicit exemplary results for several different graphs and particular decoherence processes. The limitations of the method are also discussed.

quant-ph↗

arXiv2010

Almost all quantum states have non-classical correlations

Quantum discord quantifies non-classical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord; and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension, and have direct implications on quantum computation and on the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

quant-ph↗

arXiv2009

Macroscopic bound entanglement in thermal graph states

We address the presence of bound entanglement in strongly-interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one- and two-dimensional systems are given. Our results thus prove the existence of thermal bound entanglement in an arbitrary large spin system with finite-range local interactions.

quant-ph↗

arXiv2008

Geometric phase gate on an optical transition for ion trap quantum computation

We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around 10$^{-4}$.

quant-ph↗

arXiv2008

Scaling laws for the decay of multiqubit entanglement

We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with the number of particles. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multi-particle GHZ states can generate bound entangled states.

quant-ph↗