On the capacity of a quantum perceptron for storing biased patterns

Although different architectures of quantum perceptrons have been recently put forward, the capabilities of such quantum devices versus their classical counterparts remain debated. Here, we consider random patterns and targets independently distributed with biased probabilities and investigate the storage capacity of a continuous quantum perceptron model that admits a classical limit, thus facilitating the comparison of performances. Such a more general context extends a previous study of the quantum storage capacity where using statistical mechanics techniques in the limit of a large number of inputs, it was proved that no quantum advantages are to be expected concerning the storage properties. This outcome is due to the fuzziness inevitably introduced by the intrinsic stochasticity of quantum devices. We strengthen such an indication by showing that the possibility of indefinitely enhancing the storage capacity for highly correlated patterns, as it occurs in a classical setting, is instead prevented at the quantum level.

A quantum fluctuation description of charge qubits

We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction that we describe by means of the BCS microscopic model in terms of two tunnelling superconducting systems in the strong-coupling quasi-spin formulation. Then, by means of collective observables we derive the Hamiltonian governing the quantum behaviour of the circuit in the limit of a large number N of quasi-spins. Our approach relies on suitable quantum fluctuations, i.e. on collective quasi-spin operators, different from mean-field observables, that retain a quantum character in the large-N limit. These collective operators generate the Heisenberg algebra on the circle and we show that their dynamics reproduces the phenomenological one generated by the charge qubit Hamiltonian obtained by quantizing the macroscopic classical Hamiltonian of the circuit. The microscopic derivation of the emergent, large-N behaviour provides a rigorous setting to investigate more in detail both general quantum circuits and quantum macroscopic scenarios; in particular, in the specific case of charge-qubits, it allows to explicitly obtain the temperature dependence of the critical Josephson current in the strong coupling regime, a result not accessible using standard approximation techniques.

Open Quantum Dynamics: Memory Effects and Superactivation of Backflow of Information

We investigate the divisibility properties of the tensor products (Formula presented.) of open quantum dynamics (Formula presented.) with time-dependent generators. These dynamical maps emerge from a compound open system (Formula presented.) that interacts with its own environment in such a way that memory effects remain when the environment is traced away. This study is motivated by the following intriguing effect: one can have Backflow of Information (BFI) from the environment to (Formula presented.) without the same phenomenon occurring for either (Formula presented.) and (Formula presented.). We shall refer to this effect as the Superactivation of BFI (SBFI).

Entanglement generation through Markovian feed-back in open two-qubit systems

We discuss the generation and the long-time persistence of entanglement in open two-qubit systems whose reduced dissipative dynamics is not a priori engineered but is instead subjected to filtering and Markovian feedback. In particular, we analytically study (1) whether the latter operations may enhance the environment capability of generating entanglement at short times and (2) whether the generated entanglement survives in the long-time regime. We show that, in the case of particularly symmetric Gorini-Kossakowski-Sudarshan-Lindblad it is possible to fully control the convex set of stationary states of the two-qubit reduced dynamics, therefore the asymptotic behaviour of any initial two-qubit state. We then study the impact of a suitable class of feed-back operations on the considered dynamics.

Dynamics, Information and Complexity in Quantum Systems: Second Edition

Stationary states of open XX -spin chains

We study an open quantum spin chain of arbitrary length with nearest neighbor XX interactions of strength g, immersed in an external constant magnetic field Δ along the z direction, whose end spins are weakly coupled to two heat baths at different temperatures. In the so-called global approach, namely, without neglecting interspin interactions, using standard weak-coupling limit techniques, we first derive the open chain master equation written in terms of fermionic mode operators. Then, we focus on the study of the dependence of the resulting open dynamics from the ratio rg/Δ. By increasing r, some of the chain Bohr transition frequencies become negative; when this occurs, both the generator of the dissipative time evolution and its stationary states behave discontinuously. As a consequence, the asymptotic spin and heat flows also exhibit discontinuities, but in a different way: while source terms in the spin flow continuity equation show jumps, the heat flow instead is continuous but with discontinuous first derivatives with respect to r. These two behaviors might be experimentally accessible; in particular, they could discriminate between the global and the local approaches to open quantum spin chains. Indeed, the latter one, which neglects interspin interactions in the derivation of the master equation, does not show any kind of discontinuous behavior.

Pattern capacity of a single quantum perceptron

Recent developments in quantum machine learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to establish if a quantum advantage is achievable. Here we use a statistical physics approach to compute the pattern capacity of a particular model of quantum perceptron realized by means of a continuous variable quantum system.

Local Generation of Entanglement with Redfield Dynamics

In phenomenological applications, time evolutions of Bloch-Redfield type are widely adopted for modelling open system dynamics, despite their nonpositive preserving character: this physical inconsistency, that in general shows up at small times, is usually cured by suitably restricting the space of allowed initial states. Nevertheless, additional problems may arise in relation to entanglement: specifically, we show that Redfield dynamics, though being a semigroup, can generate entanglement through a purely local action; moreover, this unphysical effect can persist on long time-scales.

Quantum state features of the FEL radiation from the occupation number statistics

The coherence of free-electron laser (FEL) radiation has so far been accessed mainly through first and second order correlation functions. Instead, we propose to reconstruct the energy state occupation number distribution of FEL radiation, avoiding the photo-counting drawbacks with high intensities, by means of maximum likelihood techniques based on the statistics of no-click events. Though the ultimate goal regards the FEL radiation statistical features, the interest of the proposal also resides in its applicability to any process of harmonic generation from a coherent light pulse, ushering in the study of the preservation of quantum features in general non-linear optical processes.

Exact Steady State of the Open XX -Spin Chain: Entanglement and Transport Properties

We study the reduced dynamics of open quantum spin chains of arbitrary length N with nearest-neighbor XX interactions, immersed within an external constant magnetic field along the z direction, the end spins of which are weakly coupled to heat baths at different temperatures, via energy-preserving couplings. We find the analytic expression of the unique stationary state of the master equation obtained in the so-called global approach based on the spectralization of the full-chain Hamiltonian. Hinging upon the explicit stationary state, we reveal the presence of sink and source terms in the spin-flow continuity equation and compare their behavior with that of the stationary heat flow. Moreover, we also obtain analytic expressions for the steady-state two-spin reduced density matrices and for their concurrence. We then set up an algorithm suited to compute the stationary bipartite entanglement along the chain and to study its dependence on the Hamiltonian parameters and on the bath temperatures.

Vibrational coherent control of localized d–d electronic excitation

Marciniak A., Marcantoni S., Giusti F., Glerean F., Sparapassi G., Nova T., Cartella A., Latini S., Valiera F., Rubio A., van den Brink J., Addressing the role of quantum coherence in the interplay between the different matter constituents (electrons, phonons and spin) is a critical step towards understanding transition metal oxides and designing complex materials with new functionalities. Here we use coherent vibrational control of on-site d–d electronic transitions in a model edge-sharing insulating transition metal oxide (CuGeO3) to single out the effects of vibrational coherence in electron–phonon coupling. By comparing time-domain experiments based on high- and low-photon-energy ultrashort laser excitation pulses with a fully quantum description of phonon-assisted absorption, we could distinguish the processes associated with incoherent thermal lattice fluctuations from those driven by the coherent motion of the atoms. In particular, while thermal fluctuations of the phonon bath uniformly increase the electronic absorption, the resonant excitation of phonon modes also results in light-induced transparency that is coherently controlled by the vibrational motion.

Entanglement and non-locality in quantum protocols with identical particles

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.

On the complete positivity of the ghirardi-rimini-weber model

We study the complete positivity of the standard, Markovian Ghirardi-Rimini-Weber model, propose an explicitly time-dependent generalization and show that in some cases one can have complete positivity even in presence of negative-rates.

Bath-assisted transport in a three-site spin chain: Global versus local approach

Within the standard weak-coupling limit, the reduced dynamics of open quantum spin chains with their two end spins coupled to two distinct heat baths at different temperatures are mainly derived using the so-called global and local approaches, in which, respectively, the spin self-interaction is and is not taken into account. In order to compare the differences between the two regimes, we concentrate on an open three-site XX spin chain, provide systematic techniques to address the global and local asymptotic states, and then compare the asymptotic spin-transport features by studying the spin flux through the middle site. Based on the analytical expressions of the stationary states in the two regimes, we find that the local approach misses important global effects emerging as spin sink and source terms that can only be due to nonnegligible interspin interactions. Moreover, we show that the local asympotic transport features cannot be recovered from the global ones by letting the interspin coupling vanish, thus pointing to the existence of different coupling ranges where only one approach is physically tenable and possibly a region where the two descriptions may coexist.

Entanglement in indistinguishable particle systems

For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the indistinguishability of identical particles hinders their individual addressability and has prompted diverse, sometimes discordant definitions of entanglement. In the present review, we provide a comparative analysis of the relevant existing approaches, which is based on the characterization of bipartite entanglement in terms of the behaviour of correlation functions. Such a point of view provides a fairly general setting where to discuss the presence of non-local effects; it is performed in the light of the following general consistency criteria: (i) entanglement corresponds to non-local correlations and cannot be generated by local operations; (ii) when, by “freezing” suitable degrees of freedom, identical particles can be effectively distinguished, their entanglement must reduce to the one that holds for distinguishable particles; (iii) in absence of other quantum resources, only entanglement can outperform classical information protocols. These three requests provide a setting that allows to evaluate strengths and weaknesses of the existing approaches to indistinguishable particle entanglement and to contribute to the current understanding of such a crucial issue. Indeed, they can be classified into five different classes: four hinging on the notion of particle and one based on that of physical modes. We show that only the latter approach is consistent with all three criteria, each of the others indeed violating at least one of them.

Time-dependent spontaneous localization processes

Time dependent Lindblad generators have mostly been studied for discrete variable open quantum systems. We hereby initiate the study of the complete positivity of a continuous one-dimensional quantum system subjected to time-dependent spatial localizations with back-flow of information.

Quasi-inversion of qubit channels

Karimipour V., In general quantum operations, or quantum channels cannot be inverted by physical operations, i.e., by completely positive trace-preserving maps. An arbitrary state passing through a quantum channel loses its fidelity with the input. Given a quantum channel E, we discuss the concept of its quasi-inverse as a completely positive trace-preserving map Eqi which when composed with E increases its average input-output fidelity in an optimal way. The channel Eqi comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples.

Two-qubit quantum probes for the temperature of an Ohmic environment

Gebbia F., Benedetti C., We address a particular instance where open quantum systems may be used as quantum probes for an emergent property of a complex system, as the temperature of a thermal bath. The inherent fragility of the quantum probes against decoherence is the key feature making the overall scheme very sensitive. The specific setting examined here is that of quantum thermometry, which aims to exploit decoherence as a resource to estimate the temperature of a sample. We focus on temperature estimation for a bosonic bath at equilibrium in the Ohmic regime (ranging from sub-Ohmic to super-Ohmic), by using pairs of qubits in different initial states and interacting with different environments, consisting either of a single thermal bath or of two independent ones at the same temperature. Our scheme involves pure dephasing of the probes, thus avoiding energy exchange with the sample and the consequent perturbation of temperature itself. We discuss the role of correlations among the probes and the presence of a local versus a global bath. We show that entanglement improves thermometry at short times if the two qubits are embedded in a common bath, whereas if the interaction time is not constrained, then coherence rather than entanglement is the key resource in quantum thermometry.

Continuous variable quantum perceptron

We present a model of Continuous Variable Quantum Perceptron (CVQP), also referred to as neuron in the following, whose architecture implements a classical perceptron. The necessary nonlinearity is obtained via measuring the output qubit and using the measurement outcome as input to an activation function. The latter is chosen to be the so-called Rectified linear unit (ReLu) activation function by virtue of its practical feasibility and the advantages it provides in learning tasks. The encoding of classical data into realistic finitely squeezed states and the use of superposed (entangled) input states for specific binary problems are discussed.

Hadamard Completely Positive Semigroups

We review the Gorini, Kossakowski, Sudarshan derivation of the generator of a completely positive norm-continuous semigroup when the constituent maps act on density matrices according to the Hadamard product rule.