The symmetrization postulate in quantum mechanics is formally reflected in the appearance of an exchange phase ruling the symmetry of identical particle global states under particle swapping. Many indirect measurements of this fundamental phase have been reported so far, while a direct observation has been only recently achieved for photons. Here we propose a general scheme capable to directly measure the exchange phase of any type of particles (bosons, fermions, anyons), exploiting the operational framework of spatially localized operations and classical communication. We experimentally implement it in an all-optical platform providing proof-of-principle for different simulated exchange phases. As a byproduct, we supply a direct measurement of the real bosonic exchange phase of photons. Also, we analyze the performance of the proposed scheme when mixtures of particles of different nature are injected. Our results confirm the symmetrization tenet and provide a tool to explore it in various scenarios.
It is shown that effects of particle identity entail reduction in the number of orbital degrees-of-freedom in non-relativistic 2-particle systems from 6 to 5. This effect of redundancy in description of orbital motion is found to be in correspondence to multiplicative phase factor $(-1)^{2s}$ which accompany interchange of the two particles, where $s$ is the spin of one particle.
Construction of multi-particle entangled states and direct teleportation of N-(spin 1/2) particles are important areas of quantum information processing. A number of different schemes which have been presented already, address the problem through controlled teleportation. In this article, a criterion based on standard quantum statistical correlations employed in the many body virial expansions is used to determine maximum entanglement for a N-particle state. These states remain entangled through proper traces to states for a smaller number of particles and can be generalized for arbitrary numb…
In the framework of Generalized probabilistic theories (GPT), we illustrate a class of statistical processes in case of two noninteracting identical particles in two modes that satisfies a well motivated notion of physicality conditions namely the double stochasticity and the no-interaction condition proposed by Karczewski et. al. (Phys. Rev. Lett. 120, 080401 (2018)), which can not be realized through a quantum mechanical process. This class of statistical process is ruled out by an additional requirement called the evolution condition imposed on two particle evolution. We also show that any …
Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as the number of particles approaches infinity. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries, and collisions between particles can be included.
A method of quantum tomography of arbitrary spin particle states is developed on the basis of the root approach. It is shown that the set of mutually complementary distributions of angular momentum projections can be naturally described by a set of basis functions based on the Kravchuk polynomials. The set of Kravchuk basis functions leads to a multi-parametric statistical distribution that generalizes the binomial distribution. In order to analyze a statistical inverse problem of quantum mechanics, we investigated the likelihood equation and the statistical properties of the obtained estimate…
For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles $\overline{n}_m$ scattered into a given ($m$-th) channel, single-channel statistics, and inter-channel correlations. We show that for initially uncorrelated particles, indistinguishability changes single channel statistics without altering the the value of $\overline{n}_m$. For uncorrelated bosons and fermions, bunching and anti-bunchin…
The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more c…
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical effect for deterministic particles, i.e. particles that have trajectories and obey deterministic dynamical equations, if one introduces a discrete time. As a demonstration of this concept we consider particle scattering on a screen with a slit. We study how resulting interference picture depends on the parameters of the model. The resulting interference pictu…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically from the classical case in which the realization probabilities are given by combinatorics. A law for the suppression of output configurations is derived and shown to apply for the majority of all possible arrangements. Such multiparticle interference effects dominate at the level of single transition amplitudes, while a generic bosonic signature can be observed…
A previous derivation of the single-particle Schrödinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schrödinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is intr…
Despite the obvious difference between fermions and bosons in their physical properties and statistical distributions, but we have to ask the following question. What is the form of statistical distribution for a system of quantum particles where any of them can be a fermion with probability [P] and can be a boson with probability [1-P]?. In this paper this question is solved
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles. In the first case, the partition function is computed and stated. In both cases, expressions for the average energy are obtained.
Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical particles in the lowest Landau level, and vortices in the Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical} statistical mechanics is shown to be a nontrivial classical limit of Haldane's exclusion statistics.
According to the identity principle in quantum theory, states of a system consisted of identical particles should maintain unchanged under interchanging between two of the particles. The whole wavefunction should be symmetrized or antisymmetrized. This leads to statistical correlations between particles, which exhibit observable effects. We design an experiment to directly observe such effects for bosons. The experiment is performed with two photons. The effect of statistical correlations is clearly observed when the wavepackets of two photons are completely overlapped, and this effect varies …
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell-Boltzmann statistics, it is not necessary to assume that the particles are distinguishable. In other words, Maxwell-Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to p…
The second virial coefficient for non-Abelian Chern-Simons particles is recalculated. It is shown that the result is periodic in the flux parameter just as in the Abelian theory.
Using results of our exact description of the spinless fermion motion in a nonhomogeneous magnetic field \( {\bf B} = B( 0, 0, 1/cosh^{2}( \frac{x-x_{0}}{ δ})) \) we study a gas of these particles moving in this field. For lower densities \( ν< ν_{c}(B, δ) \) the corresponding total energy is lower than that of the uniform field state. Thus when the density of anyons decreases a transition from the uniform statistical field state to the nonhomogeneous field state is predicted.
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential and for the multi-particle density. Three binary choices (eight routes) for the average energy are shown to be mutually consistent. An expression for the phase space function that gives the average virial pressure is derived.
A practical quantum measurement method based on the quantum nature of anti-bunching photon emission has been developed to detect single particles without the restriction of the diffraction limit. By simultane- ously counting the single-photon and two-photon signals with fluorescence microscopy, the images of nearby Nitrogen-Vacancy centers in diamond at a distance of 8.5+/-2.4 nm have been successfully reconstructed. Also their axes information was optically obtained. This quantum statistical imaging technique, with a simple exper- imental setup, can also be easily generalized in the measuring…
Chern-Simons gauge field theory has provided a natural framework to gain deep insight about many novel phenomena in two-dimensional condensed matter. We investigate the nonequilibrium thermodynamics properties of a (two-dimensional) dissipative harmonic particle when the Abelian topological gauge action and the (linear) Brownian motion dynamics are treated on an equal footing. We find out that the particle exhibits remarkable magneticlike features in the quantum domain that are beyond the celebrated Landau diamagnetism: this could be viewed as the non-relativistic Brownian counterpart of the c…
A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle exchange. One of numerous manifestations of this quantum statistics is the tendency of fermions (bosons) to anti-bunch (bunch). In a two-particle scattering experiment with two possible outgoing channels, the probability of the two particles to arrive each at a different terminal is enhanced (with respect to classical particles) for fermions, and reduced for boso…
We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that although the fluctuations of energy levels in integrable and non-integrable systems are principally different, global properties of the eigenstates may be quite similar, provided the interaction between particles exceeds some critical value. In this case the quench dynamics can be described analytically, demonstrating the universal statist…
We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics r…
We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find that the two-particle interference is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wavepacket can get completely reflected or split into a superposition of a reflected wave and an anti…
This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on many-particle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle int…
Privacy is under threat from artificial intelligence revolution fueled by unprecedented abundance of data. Differential privacy, an established candidate for privacy protection, is susceptible to adversarial attacks, acts conservatively, and leads to miss-implementations because of lacking systematic methods for setting its parameters (known as the privacy budget). An alternative is information-theoretic privacy using entropy with the drawback of requiring prior distribution of the private data. Here, by using the Fisher information, information-theoretic privacy framework is extended to avoid…
One-particle energy eigenfunctions are used to obtain quantum averages in many particle systems. These are based on the effective local field due to fixed neighbors in classical phase space, while the averages account for the non-commutativity of the position and momentum operators. Used in Monte Carlo simulations for a one-dimensional Lennard-Jones fluid, the results prove more reliable than a high temperature expansion and a harmonic local field approach, and at intermediate temperatures agree with benchmark numerical results. Results are presented for distinguishable particles, fermions, an…
