arXiv subjects

Fernando Parisio

Publications and source records attributed to Fernando Parisio.

At least 37 records · Page 2Linked to original sources

arXiv2018

Comparing experiments on quantum traversal time with the predictions of a space-time-symmetric formalism

The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that previously defined time operators, that remained within the borders of standard quantum mechanics, present some kind of pathology. Recently, a time operator acting on an additional Hilbert space has been shown to support both Hermiticity and canonical relation with an energy observable. The theory is built in a framework which treats space and time as symmetrically as possible, in the nonrelativistic regime. In this work, we use this formalism to derive a closed analytic expression for the traversal time of a quantum particle impinging on a constant-potential barrier. We test our theory in the specific experimental scenario of a realization by Rafagni et al [Appl. Phys. Lett. {\bf 58}, 774 (1991)]. The proposed approach displays a much better performance in comparison with the Büttiker-Landauer and the phase-time approximations.

quant-ph↗

arXiv2018

All bipartitions of arbitrary Dicke states

By exploiting the permutation symmetry of Dick states, we derive closed analytical expressions of Schmidt decompositions for {\it all} possible bipartitions of a system described by this kind of state. This allows us to exhaustively compute the entropy of entanglement of the bipartitions and, thus, compare the their entanglement extent. We also address the multipartite character of Dicke states by calculating the purity of balanced bipartitions to determine the potential of multipartite entanglement (the average purity). In particular, we found that the entanglement of $W$ states remains constant as the number of qubits is increased. As a final application we define a family of multipartite entanglement witnesses and compute their resistance against random and systematic imperfections. It is shown that in some circumstances, for a fixed white noise fraction, the entanglement becomes detectable only if one {\it increases} the amount of systematic imperfection in the state.

quant-ph↗

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.

quant-ph↗

arXiv2017

Critical behaviour in the optimal generation of multipartite entanglement

Two systems whose correlations cannot be classically accounted for display the simplest instance of quantum entanglement. Although this two-party association has caused a revolution in the foundations and uses of quantum mechanics, genuine entanglement among several parties unveils a whole new class of phenomena and applications. In this work we suggest a way to prepare Dicke states from a tunable source of bipartite entanglement to investigate foundational issues. The scheme has the following distinctive features: (i) it relies on controlled information loss and {\it unentangled} measurements; (ii) irrespective of the source entanglement, whenever a Dicke state is produced, it is ideal; (iii) the optimal entanglement of the bipartite source undergoes a second-order-like transition depending on the parameters of the Dicke state to be produced. These properties lead to asymptotic results on the entanglement between any qubit belonging to a Dicke state and the remaining qubits.

quant-ph↗

arXiv2017

Space-time symmetric extension of non-relativistic quantum mechanics

In quantum theory we refer to the probability of finding a particle between positions $x$ and $x+dx$ at the instant $t$, although we have no capacity of predicting exactly when the detection occurs. In this work, first we present an extended non-relativistic quantum formalism where space and time play equivalent roles. It leads to the probability of finding a particle between $x$ and $x+dx$ during [$t$,$t+dt$]. Then, we find a Schrödinger-like equation for a "mirror" wave function $ϕ(t,x)$ associated with the probability of measuring the system between $t$ and $t+dt$, given that detection occurs at $x$. In this framework, it is shown that energy measurements of a stationary state display a non-zero dispersion, and that energy-time uncertainty arises from first principles. We show that a central result on arrival time, obtained through approaches that resort to {\it ad hoc} assumptions, is a natural, built-in part of the formalism presented here.

quant-ph↗

arXiv2016

Non-ideal teleportation of tripartite entanglement: Einstein-Podolsky-Rosen versus Greenberger-Horne-Zeilinger schemes

Channels composed by Einstein-Podolsky-Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger-Horne-Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form $c_0|000\rangle+c_1|111\rangle$. The teleportation is made through measurements in the GHZ basis, and, to obtain deterministic results, in most of the investigated scenarios, four out of the eight elements of the basis need to be unambiguously distinguished. Most importantly, we show that when both, systematic errors and noise are considered, the fidelity of the teleportation protocol is higher when a GHZ channel is used in comparison to that of a channel composed by EPR pairs.

quant-ph↗

arXiv2016

Remote preparation of $W$ states from imperfect bipartite sources

Several proposals to produce {\it tripartite} $W$-type entanglement are probabilistic even if no imperfections are considered in the processes. We provide a deterministic way to remotely create $W$ states out of an EPR source. The proposal is made viable through measurements (which can be demolitive) in an appropriate three-qubit basis. The protocol becomes probabilistic only when source flaws are considered. It turns out that, even in this situation, it is robust against imperfections in two senses: (i) It is possible, after postselection, to create a pure ensemble of $W$ states out of an EPR source containing a systematic error; (ii) If no postselection is done, the resulting mixed state has a fidelity, with respect to a pure $|W\rangle$, which is higher than that of the imperfect source in comparison to an ideal EPR source. This simultaneously amounts to entanglement concentration and {\it lifting}.

quant-ph↗

arXiv2016

Quantifying the failure of Schrödinger dynamics in the free expansion of relativistic particles

It is known that Schrödinger equation fails in describing the dynamics of highly energetic particles. We propose to quantify this lack of Lorentz covariance by evaluating the probability for a particle to be measured outside the set of light cones which are compatible to its initial wave function. We consider a simple case of a particle released from a box, which, in turn, is inside a larger container. It is shown that besides the increasing error at relativistic energies, there may be a complete breakdown, with Schrödinger dynamics implying in deterministic, superluminal signaling for Lorentz factors above 129. In addition, we give an exact asymptotic expression for the violation in local causality by employing the stationary exponent method, from which the Compton wave length of the particle naturally arises as the relevant scale for the stationary points.

quant-ph↗

arXiv2016

New assessment on the nonlocality of correlation boxes

Correlation boxes are hypothetical systems capable of producing the maximal algebraic violation of Bell inequalities, beyond the quantum bound and without superluminal signaling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states has been regarded as a demonstration that the former are more nonlocal than the latter. By employing an alternative, consistent measure of nonlocality, we show that this conclusion is not necessarily true. In addition, we find a class of correlation boxes that are less nonlocal than the quantum singlet with respect to the Clauser-Horne-Shimony-Holt inequality, being, at the same time, more nonlocal with respect to the 3322 inequality.

quant-ph↗

arXiv2016

Coherent-State Overcompleteness, Path Integrals, and Weak Values

In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one can represent the closure relation in non-standard ways, in terms of a single phase-space integration of the "unlike" outer product $|z'\rangle \langle z|$, $z'\ne z$. We show that all known representations of this kind have a common ground, and that our reasoning extends to spin coherent states. These unlike identities make it possible to write formal expressions for a phase-space path integral, where the role of the Hamiltonian ${\cal H}$ is played by a weak energy value ${\cal H}_{weak}$. Therefore, in this context, we can speak of weak values without any mention to measurements. The quantity ${\cal H}_{weak}$ appears as the ruler of the phase-space dynamics in the semiclassical limit.

quant-ph↗

arXiv2016

Analytic quantification of the singlet nonlocality for the first Bell's inequality

Recently an alternative way to quantify Bell nonlocality has been proposed [Phys. Rev. A {\bf 92}, 030101(R) (2015)]. In this work we further develop this concept, the volume of violation, and analytically calculate its value for the spin-singlet state with respect to the settings of the first Bell's inequality. These settings correspond to three directions in space, or three arbitrary points on the unit sphere. It is shown that the triples of directions that lead to violations in local causality correspond to $1/3$ of all possible configurations. From the perspective of quantum communications, this means that two distant parties that were capable of align their measurements in one direction only (the remaining direction in each site being random), have a probability of about 33.3$\%$ to be able to certify their entanglement.

quant-ph↗

arXiv2015

There is no anomaly in the nonlocality of two entangled qutrits

There is no doubt about the fact that entanglement and nonlocality are distinct resources. It is acknowledged that a clear illustration of this point is the difference between maximally entangled states and states that maximally violate a Bell inequality. We give strong evidence that this anomaly may be an artefact of the measures that have been used to quantify nonlocality. By reasoning that the numeric value of a Bell function is akin to a witness rather than a quantifier, we define a measure of nonlocality and show that, for pairs of qutrits and of four-level systems, maximal entanglement does correspond to maximal nonlocality in the same scenario that gave rise to the discrepancy.

quant-ph↗

arXiv2015

Elements of a new approach to time in Quantum Mechanics

In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of a quantum system are reworked. This approach leads us to an additional concept, given by a temporal probability distribution associated with the actual measurement of an observable.

quant-ph↗

arXiv2014

Fragmentation of brittle plates by localized impact

In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over the surface. The specific probabilities employed to place the fractures come from an analysis of how the energy input propagates and dissipates over the material. The cumulative mass distributions $F(m)$ we obtain are in excellent agreement with the experimental data produced by T. Kadono [Phys. Rev. Lett. {\bf 78}, 1444 (1997)]. Particularly, in the small mass regime we get $F(m)\sim m^{-α}$, with $0.1<α<0.3$ for a quite broad range of dissipation strengths and total number of fragments. In addition we obtain the fractal dimension of the set of cracks and its correlation to the exponent $α$ that account for the experimental results given by Kadono and Arakawa [Phys. Rev. E {\bf 65}, 035107(R) (2002)].

cond-mat.soft↗

arXiv2014

Role of viscous friction in the reverse rotation of a disk

The mechanical response of a circularly-driven disk in a dissipative medium is considered. We focus on the role played by viscous friction in the spinning motion of the disk, especially on the effect called reverse rotation, where the intrinsic and orbital rotations are antiparallel. Contrary to what happens in the frictionless case, where steady reverse rotations are possible, we find that this dynamical behavior may exist only as a transient when dissipation is considered. Whether or not reverse rotations in fact occur depend on the initial conditions and on two parameters, one related to dragging, inertia, and driving, the other associated with the geometric configuration of the system. The critical value of this geometric parameter (separating the regions where reverse rotation is possible from those where it is forbidden) as a function of viscosity is well adjusted by a q-exponential function.

physics.class-ph↗

arXiv2014

Minimal Fragmentation of Regular Polygonal Plates

Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in {\it two} parts only. Contrary to what happens in the multifragmentation of a single body, minimally fragmented ensembles are often amenable to analytical treatments, while keeping key features of multifragmentation. In this work we present a study on the minimal fragmentation of regular polygonal plates with up to $100$ sides. We observe in our model the typical statistical behavior of a solid teared apart by a strong impact, for example. That is to say, a robust power law, valid for several decades, in the small mass limit. In the present case we were able to analytically determine the exponent of the accumulated mass distribution to be $\frac{1}{2}$. Less usual, but also reported in a number of experimental and numerical references on impact fragmentation, is the presence of a sharp crossover to a second power-law regime, whose exponent we found to be $\frac{1}{3}$ for an isotropic model and $\frac{2}{3}$ for a more realistic anisotropic model.

cond-mat.stat-mech↗

arXiv2013

Semiclassical Ehrenfest Paths

Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase space, directly from classical trajectories. We avoid the need of intermediate steps, like particular solutions to the Schroedinger equation or numerical integration in phase space by considering the system to be initially in a coherent state and by assuming that its early dynamics is governed by the Heller semiclassical approximation. Our result is valid for short propagation times only, but gives non-trivial information on the quantum-classical transition.

quant-ph↗

arXiv2013

Looking into the collapse of quantum states with entangled photons

We propose a scheme to investigate the time scale of the wave-function collapse by using polarization-entangled photon pairs. The setup is similar to those employed to investigate quantum correlations, but in the present case, synchronization is essential at all stages. We find that it is possible to discriminate between the scenarios of instantaneous collapse and finite-time reduction via a large number of double measurements of polarization. The quantities to be recorded would present distinct behaviors in each scenario, the deviations being small but distinguishable from pure statistical fluctuations.

quant-ph↗