International Journal of Quantum Information

We formulate Bohmian mechanics (BM) such that the main objects of concern are macroscopic phenomena, while microscopic particle trajectories only play an auxiliary role. Such a formulation makes it easy to understand why BM always makes the same measurable predictions as standard quantum mechanics (QM), irrespective of the details of microscopic trajectories. Relativistic quantum field theory (QFT) is interpreted as an effective long-distance theory that at smaller distances must be replaced by some more fundamental theory. Analogy with condensed-matter physics suggests that this more fundamental theory could have a form of nonrelativistic QM, offering a simple generic resolution of an apparent conflict between BM and relativistic QFT.

It is convenient to describe a quantum system at all times by means of a “history operator” $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the “sum over position histories” of the Feynman path-integral. As we argue in this work, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by $C$ modifies the history operator, $C\to PC$, where $P$ is the projector corresponding to the measurement. We refer to this modification as “history operator collapse”. Thus, $C$ keeps track of the succession of measurements on a system, and contains all histories compatible with the results of these measurements. The collapse modifies the history content of $C$, and therefore modifies also the past (relative to the measurement), but never in a way to violate causality. Probabilities of outcomes are obtained as $\mathrm{\text{Tr}}(C^{†}PC)∕\mathrm{\text{Tr}}(C^{†}C)$. A similar formula yields probabilities for intermediate measurements, and reproduces the result of the two-vector formalism in the case of the given initial and final states. We apply the history operator formalism to a few examples: entangler circuit, Mach–Zehnder interferometer, teleportation circuit and three-box experiment. Not surprisingly, the propagation of coordinate eigenstates $|q〉$ is described by a history operator $C$ containing the Feynman path-integral.

In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’tHooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

The interaction of a quantum particle with a gaseous detector is studied in the quantum-mechanical state space of the particle-detector system by means of a simple stationary scattering 3D model. The particle is assumed to interact with $N$ two-level point-like scatterers depicting the atoms of the detector. Due to the contact interaction, the particle scatters off the atoms in isotropic spherical waves. Remarkably, the Lippmann–Schwinger equation of this multiple scattering problem can be exactly solved in a nonperturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors. It is shown that the differential cross-section of excitation must be large enough in the forward direction to get the formation of tracks. In addition, the relatively small influence of atomic positions is highlighted. These results are explained through a perturbative calculation.

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin $1∕2$ states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

The quest for a microscopic foundation of thermodynamics is addressed within the Nonunitary Newtonian Gravity (NNG) model through the study of a specific closed system, namely, a three-dimensional harmonic nanocrystal. A numerical calculation of the nanocrystal von Neumann entropy as a function of time is performed, showing a sharp monotonic increase, followed by a stabilization at late times. This behavior is consistent with the emergence of a microcanonical ensemble within the initial energy levels, signaling, in this way, the establishment of a nonunitary gravity-induced thermal equilibrium.

We propose a mixedness quantifier based on entropy fluctuations. It provides information about the degree of mixedness either for finite dimensional and infinite dimensional Hilbert spaces (HS). It may be used to determine the reduction of the HS as it becomes maximum when either the state is maximally mixed, or when the HS effectively reduces its dimensions, such as in the atom field interaction where the two-level atom dictates the final dimension of the field.

The success of quantum noise sensing methods depends on the optimal interplay between properly designed control pulses and statistically informative measurement data on a specific quantum-probe observable. To enhance the information content of the data and reduce as much as possible the number of measurements on the probe, the filter orthogonalization method has been recently introduced. The latter is able to transform the control filter functions on an orthogonal basis allowing for the optimal reconstruction of the noise power spectral density. In this paper, we formalize this method within the standard formalism of minimum mean squared error estimation and we show the equivalence between the solutions of the two approaches. Then, we introduce a nonnegative least squares formulation that ensures the nonnegativeness of the estimated noise spectral density. Moreover, we also propose a novel protocol for the design in the frequency domain of the set of filter functions. The frequency-designed filter functions and the nonnegative least squares reconstruction are numerically tested on noise spectra with multiple components and as a function of the estimation parameters.

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.

In this work, quantum metrology techniques are applied to the imaging of objects with a nonuniform refractive spatial profile. A sensible improvement on the classical accuracy is shown to be found when the “Twin Beam (TWB) State” is used. In particular, exploiting the multimode spatial correlation, naturally produced in the Parametric Down Conversion (PDC) process, allows a 2D reconstruction of complex spatial profiles, thus enabling an enhanced imaging. The idea is to use one of the spatially multimode beams to probe the sample and the other as a reference to reduce the noise. A similar model can also be used to describe wave front distortion measurements. The model is meant to be followed by a first experimental demonstration of such enhanced measurement scheme.

Collapse models consist in dynamical reformulations of the standard quantum mechanics aiming to solve the measurement problem. The standard Schrödinger dynamics is modified with the introduction of nonlinear and stochastic terms, which induce the wave function collapse in space. Collapse models predict slight deviations from the standard quantum mechanics predictions, in particular the emission of a “spontaneous radiation”, which we explored to set the most stringent limits on the collapse models parameters in a broad range. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by the theories. The results of the data analyses, and the ongoing experimental efforts will be presented.

We analyze the effects of some stochastic deviations from the ideal response in silicon photomultipliers that prove to be detrimental for the measurement of quantum properties of light. We demonstrate that an optimized operation mode can overcome some limitations of the detectors allowing the characterization of entanglement in mesoscopic twin-beam states.