M. Blasone, F. Dell'Anno, S. De Siena, F. Illuminati
We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
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The phenomena of particle mixing and flavor oscillations in elementary particle physics can be addressed by the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the st…
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signat…
We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrate some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and tha…
We investigate and quantify various measures of bipartite and tripartite entanglement in the context of two and three flavor neutrino oscillations. The bipartite entanglement is analogous to the entanglement swapping resulting from a beam splitter in quantum optics. For the three neutrino systems various measures of tripartite entanglement are explored. The significant result is that a monogamy inequality in terms of negativity leads to a residual entanglement, implying true tripartite entanglement in the three neutrino system. This leads us to an analogy of the three neutrino state with a gen…
Mixing transformations in quantum field theory are non-trivial, since they are intimately related to the unitary inequivalence between Fock spaces for fields with definite mass and fields with definite flavor. Considering the superposition of two neutral scalar (spin-0) bosonic fields, we investigate some features of the emerging condensate structure of the flavor vacuum. In particular, we quantify the flavor vacuum entanglement in terms of the von Neumann entanglement entropy of the reduced state. Furthermore, in a suitable limit, we show that the flavor vacuum has a structure akin to the the…
In this paper, we consider the quantum correlations, coherence and entanglement, in neutrino oscillation. We find that the $l_{1}$-norm as a coherence measure is equal to sum of the three possible concurrences for measuring the entanglement among different flavor modes which were calculated in the paper by (M. Blasone et al., Europhys. Lett., {\bf 112}, 20007). Our result shows that the origin of the flavor entanglement in neutrino oscillation is the same as that of quantum coherence. Furthermore, in the wave packet framework, the variation of $l_{1}$-norm is investigated by varying the wave p…
We theoretically show that bright six-partite continuous-variable entanglement can be generated using cascaded four-wave mixing effects of third-order nonlinearity atomic systems above threshold. The six-partite continuous-variable entanglement among the six cavity fields with different frequencies is analyzed by applying optimized inseparability criteria proposed by Van Loock and Furusawa.
Quantum speed limit time for bipartite entanglement in neutrino oscillations in matter with nonstandard interactions
研究中微子在物质中非标准相互作用下的双粒子纠缠量子速度限制时间，揭示NSI参数对纠缠演化的影响。
We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.
Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the non-linear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the …
We suggest and demonstrate a method to assess entanglement generation schemes based on mixing of Gaussian states at a beam splitter (BS). Our method is based on the fidelity criterion and represents a tool to analyze the effect of losses and noise before the BS in both symmetric and asymmetric channels with and without thermal effects. More generally, our scheme allows one to pre-assess entanglement resources and to optimize the design of BS-based schemes for the generation of continuous variable entanglement.
Flavor oscillations in elementary particle physics are related to multi-mode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states …
We propose an approach to generate strong quantum entanglement by the controllable four wave mixing mechanism in a single cavity, weak coupling optomechanical system. The optomechanical system is driven by a strong two tone pump field and a weak signal field, simultaneously. The two tone pump field consists of a lower and an upper sideband, which couple with the optical cavity and mechanical resonator, and generate the beam splitter and two mode squeezing interactions under the rotating wave approximation. This interaction mechanism modifies the effective susceptibility of the optomechanical c…
Possibilities of generation of lower order and higher order intermodal entanglement in 87Rb 5S-5P-5D hyperfine manifold are rigorously investigated using Sen-Mandal perturbative technique by showing the equivalence of the system with the four-wave mixing (FWM) process. The investigation has revealed that for a set of experimentally realizable/relevant parameters we can observe lower order and higher order intermodal entanglement between pump and signal modes, signal and idler modes, and idler and pump modes in a FWM process associated with the 87Rb 5S-5P-5D hyperfine manifold. In addition, tri…
The dispersive interaction of atoms and a far-detuned light field allows nondestructive imaging of the density oscillations in Bose-Einstein condensates. Starting from a ground state condensate, we investigate how the measurement back action leads to squeezing and entanglement of the quantized density oscillations. In particular, we show that properly timed, stroboscopic imaging and feedback can be used to selectively address specific eigenmodes and avoid excitation of non-targeted modes of the system.
We investigate the importance of going beyond the mean-field approximation in the dynamics of collective neutrino oscillations. To expand our understanding of the coherent neutrino oscillation problem, we apply concepts from many-body physics and quantum information theory. Specifically, we use measures of nontrivial correlations (otherwise known as "entanglement") between the constituent neutrinos of the many-body system, such as the entanglement entropy and the Bloch vector of the reduced density matrix. The relevance of going beyond the mean field is demonstrated by comparisons between the …
We characterize correlations in polarization and time of photon pairs generated from a cold cloud of Rb-87 atoms via a four-wave mixing process in a cascade level scheme. Quantum state tomography reveals entangled polarization states of high purity for each of the decay paths through two different intermediate hyperfine levels. When allowing both decay paths, we observe quantum beats in time-resolved correlation measurements.
We investigate the nonlinear interaction between two photons in a single input pulse at an atomic two level nonlinearity. A one dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric downconversion. A method of generating photon pairs from coherent pump light using this quantum mechanical four wave mixing process is proposed.
Entanglement of a quantum system depends upon relative phase in complicated ways, which no single measurement can reflect. Because of this, entanglement witnesses are necessarily limited in applicability and/or utility. We propose here a solution to the problem using quantum neural networks. A quantum system contains the information of its entanglement; thus, if we are clever, we can extract that information efficiently. As proof of concept, we show how this can be done for the case of pure states of a two-qubit system, using an entanglement indicator corrected for the anomalous phase oscillat…
We present the measurement of entanglement between twin beams generated with a doubly resonant optical parameter oscillator (OPO) based on four-wave mixing in hot $^{85}$Rb vapor above threshold. This is the first measurement of entanglement in an OPO with $χ^{(3)}$ media above threshold. We reconstruct the covariance matrix for several configurations and with a full picture of the four side band mode state, we study entanglement between all possible bi-partitions. We show a robust generation of entanglement with stronger generation for a specific pair of modes. For this system, we show that a…
We suggest and demonstrate an all-optical experimental setup to observe and engineer entanglement oscillations of a pair of polarization qubits in a non-Markovian channel. We generate entangled photon pairs by spontaneous parametric downconversion (SPDC), and then insert a programmable spatial light modulator in order to impose a polarization dependent phase-shift on the spatial domain of the SPDC output and to create an effective non-Markovian environment. Modulation of the enviroment spectrum is obtained by inserting a spatial grating on the signal arm. In our experiment, programmable oscill…
This paper reports 1.5-um band time-bin entanglement generation. We employed a spontaneous four-wave mixing process in a dispersion shifted fiber, with which correlated photon pairs with very narrow bandwidths were generated efficiently. To observe two-photon interference, we used planar lightwave circuit based interferometers that were operated stably without feedback control. As a result, we obtained coincidence fringes with 99 % visibilities after subtracting accidental coincidences, and successfully distributed entangled photons over 20-km standard single-mode fiber without any deteriorati…
Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded (DELC) four-wave mixing (FWM) processes are proposed to generate all-optical controlled multipartite entanglement within a single device. The entanglement characteristics of the produced states of light are characterized by applying the Duan criterion and the positivity under partial transposition criterion. Moreover, by using an internal dressing field to modulate atomic coherence, multiple quantum coherent channels of FWM are simultaneously const…
This paper has been withdrawn since it was an inadvertant double submission. An updated version of the original submission can be found at quant-ph/0505131
We study the time evolution of quantum entanglement between an electron and its parent ion during the rescattering due to a strong few-cycle laser pulse. Based on a simple one-dimensional model, we compute the Neumann entropy during the process for several values of the carrier-envelope phase. The local maxima of the oscillations in the Neumann entropy coincide with the zero crossings of the electric field of the laser pulse. We employ the Wigner function to qualitatively explain the quantum dynamics of rescattering in the phase space.
The phase transition to mirrorless oscillation in resonantly enhanced four-wave mixing in double-$Λ$ systems are studied analytically for the ideal case of infinite lifetimes of ground-state coherences. The stationary susceptibilities are obtained in all orders of the generated fields and analytic solutions of the coupled nonlinear differential equations for the field amplitudes are derived and discussed.
In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one has to usually work in a regime where the information aquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not crit…
We study dynamics of quantum entanglement in smooth global quenches with a finite rate, by computing the time evolution of entanglement entropy in 1 + 1 dimensional free scalar theory with time-dependent masses which start from a nonzero value at early time and either crosses or approaches zero. The time-dependence is chosen so that the quantum dynamics is exactly solvable. If the quenches asymptotically approach a critical point at late time, the early-time and late-time entropies are proportional to the time and subsystem size respectively. Their proportionality coefficients are determined b…
The violation of Leggett-Garg inequalities tested the quantumness of neutrino oscillations (NOs) across macroscopic distances. The quantumness can be quantified by using the tools of the quantum resource theories. Recently, a new genuine tripartite entanglement measure [S. B. Xie et al., Phys. Rev. Lett. 127, 040403 (2021)], concurrence fill, is defined as the square root of the area of the concurrence triangle satisfying all genuine multipartite entanglement conditions. It has several advantages compared to other existing tripartite measures. Here, we focus on using concurrence fill to quanti…
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in details the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density entanglemen…
We demonstrate an efficient nonlinear process in which Stokes and anti-Stokes components are generated spontaneously in a Raman-like, near resonant media driven by low power counter-propagating fields. Oscillation of this kind does not require optical cavity and can be viewed as a spontaneous formation of atomic coherence grating.
This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of t…
Using four-wave mixing in a hot atomic vapor, we generate a pair of entangled twin beams in the microsecond pulsed regime near the D1 line of $^{85}$Rb, making it compatible with commonly used quantum memory techniques. The beams are generated in the bright and vacuum-squeezed regimes, requiring two separate methods of analysis, without and with local oscillators, respectively. We report a noise reduction of up to $3.8\pm 0.2$ dB below the standard quantum limit in the pulsed regime and a level of entanglement that violates an Einstein--Podolsky--Rosen inequality.
We show that a novel optical parametric oscillator, based on concurrent $χ^{(2)}$ nonlinearities, can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are {\em two} ways that the system can exhibit a new three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extra-cavity fluctuation spectra that may be measured to verify our predictions.
The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle mixing can be obtained if one investigates the behavior of quantum correlations associated to flavor oscillations. By identifying the neutrino three-flavor modes with (suitably defined) three-qubit modes, the exploitation of tools of quantum information theory for mixed states allows a detailed analysis of the dynamical behavior of flavor enta…
Entanglement Oscillations from Many-Body Quantum Scars
本文研究了多体量子疤痕模型中纠缠动力学的差异，通过无路定理解释了部分模型中纠缠完全冻结的现象，并提出了一种形变模型以规避该定理的方法。
The two-particle wave function of neutrino and recoil nucleus is found as a solution of an initial value problem in the far zone for a time longer than the electron capture decay lifetime of a hydrogenlike ion. The neutrino-recoil entanglement arising in such a process is a consequence of the momentum conservation and is closely related to the wave packet structure of the state. Because of neutrino mixing, the joint wave packet involves the coherent superposition of the neutrino mass eigenstate packets. This is the new physical realization of the Einstein-Podolsky-Rosen thought experiment, whi…
Characterizing Entanglement in Combinations of Bell States through Superposition and Mixing: An Increase in Entanglement on Introducing Depolarizing, Phase Damping, and Amplitude Damping Noise
该研究表征两量子比特贝尔态组合在三种退相干信道下的纠缠，发现特定参数下增噪可提升并发度，明确纠缠与非局域性边界，为NISQ架构的纠缠管理提供分析参考。
In environments such as core-collapse supernovae, neutron star mergers, or the early universe, where the neutrino fluxes can be extremely high, neutrino-neutrino interactions are appreciable and contribute substantially to their flavor evolution. Such a system of interacting neutrinos can be regarded as a quantum many-body system, and prospects for nontrivial quantum correlations, i.e., entanglement, developing in a gas of interacting neutrinos have been investigated previously. In this work, we uncover an intriguing connection between the entropy of entanglement of individual neutrinos with t…
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
We show that initially localized and uncorrelated two-particles quantum wavepackets evolving in a one-dimensional discrete lattice become strongly entangled while drifting under the action of an harmonic AC field resonant with doubled Bloch oscillations promoted by a static DC field. Although partial entanglement is achieved when the AC field is resonant with the single-particle Bloch oscillations, it is strongly limited by the survival of anti-correlated unbounded states. We further show that the phase dependence of the wavepacket centroid velocity is similar to the semiclassical behavior dep…
We investigate the entanglement arising naturally in a 1D Ising chain in a magnetic field in an arbitrary direction. We find that for different temperatures, different orientations of the magnetic field give maximum entanglement. In the high temperature limit, this optimal orientation corresponds to the magnetic field being perpendicular to the Ising orientation (z direction). In the low temperature limit, we find that varying the angle of the magnetic field very slightly from the z direction leads to a rapid rise in entanglement. We also find that the orientation of the magnetic field for max…
We demonstrate theoretically and experimentally a high level of control of the four-wave mixing process in an inert gas filled inhibited-coupling guiding hollow-core photonic crystal fiber in order to generate photon pairs. The specific multiple-branch dispersion profile in such fibers allows both entangled and separable bi-photon states to be produced. By controlling the choice of gas, its pressure and the fiber length, we experimentally generate various joint spectral intensity profiles in a stimulated regime that is transferable to the spontaneous regime. The generated profiles cover both s…
Reconfigurable entanglement distribution network based on pump management of spontaneous four-wave mixing source
提出基于SFWM源可调谐多泵浦激励与时分方法的可重构纠缠分发网络，实验表征双光子相关性，并演示10用户全连接QKD网络。
Four-wave mixing in atomic vapor allows for the generation of multi-spatial-mode states of light containing many pairs of two-mode entangled vacuum beams. This in principle can be used to send independent secure keys to multiple parties simultaneously using a single light source. In our experiment, we demonstrate this spatial multiplexing of information by selecting three independent pairs of entangled modes and performing continuous-variable measurements to verify the correlations between entangled partners. In this way, we generate three independent pairs of correlated random bit streams tha…
We show that mode-mixing quantum gates can be produced by non-uniform relativistic acceleration. Periodic motion in cavities exhibits a series of resonant conditions producing entangling quantum gates between different frequency modes. The resonant condition associated with particle creation is the main feature of the dynamical Casimir effect which has been recently demonstrated in superconducting circuits. We show that a second resonance, which has attracted less attention since it implies negligible particle production, produces a beam splitting quantum gate leading to a resonant enhancement…
Interference comes from coherent mixing. It can be suppressed by entanglement, and the latter can be erased so as to revive interference. If the entanglement is a mimal-term one (with minimal-term mixing), as is the case in most thought and real experiments reported, there appears the possibility of counter erasure and counter interference. This peculiar phenomenon of minimal-term mixing and minimal-term entanglement is investigated in detail. In particular, all two-term mixings of an (arbitrary) given minimal-term mixed state are explicitly exhibited. And so are their possible laboratory real…
We theoretically investigate a scheme for atom interferometry that surpasses the standard quantum limit. A four-wave mixing scheme similar to the recent experiment performed by Pertot et al. \cite{pertot} is used to generate sub-shot noise correlations between two modes. These two modes are then interfered with the remaining two modes in such a way as to surpass the standard quantum limit, whilst utilising all of the available atoms. Our scheme can be viewed as using two correlated interferometers. That is, the signal from each interferometer when looked at individually is classical, but there…
In quantum optics a pure state is considered classical, relative to the statistics of photodetection, if and only if it is a coherent state. A different and newer notion of nonclassicality is based on modal entanglement. One example that relates these two notions is the Hong-Ou-Mandel effect, where modal entanglement is generated by a beamsplitter from the nonclassical photon-number state. This suggests that beamsplitters or, more generally, linear-optical networks are mediators of the two notions of nonclassicality. In this Brief Report, we show the following: Given a nonclassical pure-produc…
We investigate the quantum transport in a generalized N-particle Hanbury Brown--Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. It dictates, for example, that the degree of entanglement of a photon pair in a Bell state remains maximally entangled during propagation in free-space. Here we outline a scenario where this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and pro…
We analyse particle creation and mode mixing for a quantum field in an accelerated cavity, assuming small accelerations but allowing arbitrary velocities, travel times and travel distances, and in particular including the regime of relativistic velocities. As an application, we identify a desktop experimental scenario where the mode mixing resonance frequency in linear sinusoidal motion or in uniform circular motion is significantly below the particle creation resonance frequencies of the Dynamical Casimir Effect, and arguably at the threshold of current technology. The mode mixing acts as a b…
Efficient Entanglement Manipulation Cookbook: From Mixing to a Computational Second Law
本文系统分析两种计算纠缠测度的基本性质，引入上下界扩展，研究凸性、凹性、可加性及局部酉不变性，证明其仅在高效LOCC信道下为LOCC单调。
Collective neutrino oscillations play a crucial role in transporting lepton flavor in astrophysical settings like supernovae and neutron star binary merger remnants, which are characterized by large neutrino densities. In these settings, simulations in the mean-field approximation show that neutrino-neutrino interactions can overtake vacuum oscillations and give rise to fast collective flavor evolution on time-scales $t\proptoμ^{-1}$, with $μ$ proportional to the local neutrino density. In this work, we study the full out-of-equilibrium flavor dynamics in simple multi-angle geometries displayi…
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