The archetypal quantum interferometry experiment yields an interference pattern that results from the indistinguishability of two spatiotemporal paths available to a photon or to a pair of entangled photons. A fundamental challenge in quantum interferometry is to perform such experiments with a higher number of paths, and over large distances. In particular, the distribution of such highly entangled states in long-haul optical fibers is one of the core concepts behind quantum information networks. We demonstrate that using indistinguishable frequency paths instead of spatiotemporal ones allows for robust, high-dimensional quantum interferometry in optical fibers. In our system, twin-photons from an Einstein-Podolsky-Rosen (EPR) pair are offered up to 9 frequency paths after propagation in long-haul optical fibers, and we show that the multi-path quantum interference patterns can be faithfully restored after the photons travel a total distance of up to 60 km.

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as $A$ and $B$, is computed analytically using a Coulomb gas method. It is shown that this probability, for large $N$, goes as $\exp[-\beta N^2\Phi(\zeta)]$, where the parameter $\beta$ is the Dyson index of the ensemble, $\zeta$ is the large deviation parameter while the rate function $\Phi(\zeta)$ is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems $1$ and $2$, obtained by further partitioning the subsystem $A$, using the properties of the density matrix's partial transpose $\rho_{12}^\Gamma$. The density of states of $\rho_{12}^\Gamma$ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter $\zeta$. Log negativity is used to quantify the entanglement between subsystems $1$ and $2$. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Discrete time crystals are a recently proposed and experimentally observed out-of-equilibrium dynamical phase of Floquet systems, where the stroboscopic evolution of a local observable repeats itself at an integer multiple of the driving period. We address this issue in a driven-dissipative setup, focusing on the modulated open Dicke model, which can be implemented by cavity or circuit QED systems. In the thermodynamic limit, we employ semiclassical approaches and find rich dynamical phases on top of the discrete time-crystalline order. In a deep quantum regime with few qubits, we find clear signatures of a transient discrete time-crystalline behavior, which is absent in the isolated counterpart. We establish a phenomenology of dissipative discrete time crystals by generalizing the Landau theory of phase transitions to Floquet open systems.

We derived stochastic master equation for a system interacting with the Bose field prepared in a superposition of coherent states. We use the model of repeating interactions and measurements with the environment given by an infinite chain of identical and not interacting between themselves quantum systems being harmonic oscillators. Elements of the environment chain interact with the quantum system in turn one by one and they are subsequently measured. We determined the conditional evolution of the quantum system for the continuous in time observations as a limit of discrete recurrence equations.

We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators, $\langle O_1 \rangle$ and $\langle O_2 \rangle$, but may not have access to $\langle O_1 O_2 \rangle$. This problem is relevant for the study of localized quantum information in gravity since the set of approximately-local operators in a region may not be closed under arbitrary products. While we cannot naturally associate a density matrix with a state in this setting, it is still possible to define a modular operator for a state, and distinguish between two states using a relative modular operator. These operators are defined on a little Hilbert space, which parameterizes small deformations of the system away from its original state, and they do not depend on the structure of the full Hilbert space of the theory. We extract a class of relative-entropy-like quantities from the spectrum of these operators that measure the distance between states, are monotonic under contractions of the set of available observables, and vanish only when the states are equal. Consequently, these distance-measures can be used to define measures of bipartite and multipartite entanglement. We describe applications of our measures to coarse-grained and fine-grained subregion dualities in AdS/CFT and provide a few sample calculations to illustrate our formalism.

In this work we construct tests that allow a classical user to certify high dimensional entanglement in uncharacterized and possibly noisy quantum devices. We present a family of non-local games $\{G_n\}$ that for all $n$ certify states with entanglement of formation $\Omega(n)$. These tests can be derived from any bipartite non-local game with a classical-quantum gap. Furthermore, our tests are noise-tolerant in the sense that fault tolerant technologies are not needed to play the games; entanglement distributed over noisy channels can pass with high probability, making our tests relevant for realistic experimental settings. This is in contrast to, e.g., results on self-testing of high dimensional entanglement, which are only relevant when the noise rate goes to zero with the system's size $n$. As a corollary of our result, we supply a lower-bound on the entanglement cost of any state achieving a quantum advantage in a bipartite non-local game. Our proof techniques heavily rely on ideas from the work on classical and quantum parallel repetition theorems.

Entanglement sources that produce many entangled states act as a main component in applications exploiting quantum physics such as quantum communication and cryptography. Realistic sources are inherently noisy, cannot run for an infinitely long time, and do not necessarily behave in an independent and identically distributed manner. An important question then arises -- how can one test, or certify, that a realistic source produces high amounts of entanglement? Crucially, a meaningful and operational solution should allow us to certify the entanglement which is available for further applications after performing the test itself (in contrast to assuming the availability of an additional source which can produce more entangled states, identical to those which were tested). To answer the above question and lower bound the amount of entanglement produced by an uncharacterised source, we present a protocol that can be run by interacting classically with uncharacterised (but not entangled to one another) measurement devices used to measure the states produced by the source. A successful run of the protocol implies that the remaining quantum state has high amounts of one-shot distillable entanglement. That is, one can distill many maximally entangled states out of the single remaining state. Importantly, our protocol can tolerate noise and, thus, certify entanglement produced by realistic sources. With the above properties, the protocol acts as the first "operational device-independent entanglement certification protocol" and allows one to test and benchmark uncharacterised entanglement sources which may be otherwise incomparable.

We discuss the preceding Comment and conclude that the arguments given there against the relevance of null weak values as representing the absence of a system property are not compelling. We give an example in which the transition matrix elements that make the projector weak values vanish are the same ones that suppress detector clicks in strong measurements. Whether weak values are taken to account for the past of a quantum system or not depend on general interpretional commitments of the quantum formalism itself rather than on peculiarities of the weak measurements framework.

We report on the luminescence's life-time and line-width from an array of individual quantum dots; these were interfaced with graphene surface guides or dispersed on a metal film. Our results are consistent with screening by charge carriers. Fluorescence quenching is typically mentioned as a sign that chromophores are interfacing a conductive surface; we found that QD interfaced with conductive layers exhibited shorter life-time and line-broadening but not necessarily fluorescence quenching as the latter may be impacted by molecular concentration, reflectivity and conductor imperfections. We also comment on selective life-time measurements, which, we postulate depend on the specifics of the local density-of-states involved.

According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev--Mickelsson anomaly which obstructs the renormalization of Yang--Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos theoretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.

We present serial-parallel conversion for a heralded single photon source (heralded SPS). We theoretically show that with the heralding signal, the serial-parallel converter can route a stream of n photons to n different spatial modes more efficiently than is the case without using a heralding signal. We also experimentally demonstrate serial-parallel conversion for two photons generated from a heralded SPS. We achieve a conversion efficiency of 0.533 \pm 0.003, which exceeds the maximum achievable efficiency of 0.5 for serial-parallel conversion using unheralded photons, and is double the efficiency (0.25) for that using beamsplitters. When the losses in the optical converter are corrected for, the efficiency of the current setup can be increased up to 0.996 \pm 0.006.

We propose a refinement of the Robertson-Schrodinger uncertainty principle (RSUP) using Wigner distributions. This new principle is stronger than the RSUP. In particular, and unlike the RSUP, which can be saturated by many phase space functions, the refined RSUP can be saturated by pure Gaussian Wigner functions only. Moreover, the new principle is technically as simple as the standard RSUP. In addition, it makes a direct connection with modern harmonic analysis, since it involves the Wigner transform and its symplectic Fourier transform, which is the radar ambiguity function. As a by-product of the refined RSUP, we derive inequalities involving the entropy and the covariance matrix of Wigner distributions. These inequalities refine the Shanon and the Hirschman inequalities for the Wigner distribution of a mixed quantum state $\rho$. We prove sharp estimates which critically depend on the purity of $\rho$ and which are saturated in the Gaussian case.

We investigate the non-Markovian dynamics of a qubit-oscillator system embedded in a noisy environment by employing the hierarchical equations of motion approach. It is found that the decoherence rate of the whole qubit-oscillator-bath system can be significantly suppressed by enhancing the coupling strength between the qubit and the harmonic oscillator. Moreover, we find that the non-Markovian memory character of the bath is able to facilitate a robust quantum coherent dynamics in this qubit-oscillator-bath system. Our findings may be used to engineer some tunable coherent manipulations in mesoscopic quantum circuits.

We report the experimental study of a harmonic oscillator in the relativistic regime. The oscillator is composed of Bose-condensed lithium atoms in the third band of an optical lattice, which have an energy-momentum relation nearly identical to that of a massive relativistic particle, with a reduced effective mass and speed of light. Imaging the shape of oscillator worldlines at velocities up to 98% of the effective speed of light reveals a crossover from sinusoidal to nearly photon-like propagation. Effective time dilation causes the measured period of oscillations to increase with energy; our measurements reveal beyond-leading-order contributions to this relativistic anharmonicity. Preparing oscillator ensembles, we observe an intrinsic relativistic dephasing and a breathing mode with exactly the opposite phase of that predicted for non-relativistic harmonic motion. All observed dynamics are in quantitative agreement with longstanding relativistic predictions.

We propose a scheme to detect analog Hawking radiation (HR) in an atomic Bose-Einstein condensate (BEC) through measuring the diffusion of a dark soliton. The HR is generated by changing the transverse trapping potential of the BEC to obtain a background flow, which is subsonic in downstream and supersonic in upstream, satisfying the condition of black hole horizon. When the system is in thermal equilibrium at Hawking temperature, a dark soliton is created in the upstream. Due to the influence of the HR, the motion of the dark soliton is similar to a Brownian particle and hence exhibits an apparent diffusion, which can be measured and be taken as a signal of the HR. Since the dark soliton is much "heavier" than Hawking quanta, its diffusion is much easier detectable than the Hawking quanta themselves.

Resonant spontaneous bremsstrahlung of an electron scattered by a nucleus in the field of two moderately strong pulsed laser waves is studied theoretically. The process is studied in detail within the interference kinematic region. This region is determined by scattering of particles in the same plane at predetermined angles, at that stimulated absorption and emission of photons of external pulsed waves by an electron occurs in correlated manner. The correspondence between the emission angle and the final-electron energy is established in the kinematic region where the resonant parametric interference effect is manifested. The resonant differential cross section of ENSB process with simultaneous registration of both emission angles of the spontaneous photon and the scattered electron, can exceed by 4-5 orders of magnitude the corresponding cross section in the absence of an external field. It was shown for nonrelativistic electrons that the resonant cross section of ENSB in the field of two pulsed laser waves within the interference region in two order of magnitude may exceed corresponding cross section in the Bunkin-Fedorov kinematic region. The obtained results may be experimentally verified, for example, by scientific facilities at sources of pulsed laser radiation (SLAC, FAIR, XFEL, ELI).

Intrinsic quantum correlations supported by the $SU(2)\otimes SU(2)$ structure of the Dirac equation used to describe particle/antiparticle states, optical ion traps and bilayer graphene are investigated and connected to the description of local properties of Dirac bi-spinors. For quantum states driven by Dirac-like Hamiltonians, quantum entanglement and geometric discord between spin and parity degrees of freedom - sometimes mapped into equivalent low energy internal degrees of freedom - are obtained. Such \textit{spin-parity} quantum correlations and the corresponding nonlocal intrinsic structures of bi-spinor fermionic states can be classified in order to relate quantum observables to the (non)local behavior of these correlations. It is shown that free particle mixed states do not violate the Clauser-Horne-Shymony-Holt inequality: the correlations in such mixed bi-spinors, although quantum, can be reproduced by a suitable local hidden variable model. Additionally, the effects due to a non-minimal coupling to a homogeneous magnetic field, and to the inclusion of thermal effects are evaluated, and quantum correlations of associated quantum mixtures and of the thermal states are all quantified.The above-mentioned correlation quantifiers are then used to measure the influence of CP transformations on \textit{spin-parity} quantum correlations, and our results show that quantum entanglement is invariant under CP transformations, although the geometric discord is highly sensitive to the CP symmetry.

The theoretical method to study strong coupling between an ensemble of quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster has been presented by using a rigorous first-principles electromagnetic Green's tensor technique. We have demonstrated that multi-qubit entanglement for two-level QEs can be produced at different frequencies simultaneously, when they locate in hot spots of metallic nanoparticle clusters. The duration of quantum beats for such an entanglement can reach two orders longer than that for the entanglement in a photonic cavity. The phenomenon originates from collective coupling resonance excitation of the cluster. At the frequency of single scattering resonance, the entanglement cannot be produced although the single QE spontaneous decay rate is very big

We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs is also reported. The proposed scheme is analysed with experimentally realistic parameters, making it a promising mean to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.

We produced optical waveguides in the 167Er3+ :7LiYF4 crystal with diameters ranging from 30 to 100 mkm by using the depressed-cladding approach with femtosecond laser. These waveguides were studied (both inside and outside) by stationary and coherent spectroscopy on the 809 nm optical transitions between the hyperfine sublevels of 4I15/2 and 4I9/2 multiplets of 167Er3+ ions. It was found that the spectra of 167Er3+ were slightly broadened and shifted inside the waveguides compared to the bulk crystal spectra. We managed to observe a two-pulse photon echo on this transition and determined phase relaxation times for each of waveguides. The experimental results show that the created crystal waveguides doped by rare-earth ions can be used in optical quantum memory and integrated quantum schemes.