Papers

We introduce a two-dimensional model of spin-1/2 Dirac fermions in graphene subjected to a highly tunable electric field, which exhibits super-Klein tunneling. The electric field can be continuously interpolated between two limiting configurations: a uniform electrostatic Lorentzian barrier with translational invariance and a chain of well-separated electrostatic scatterers. We demonstrate that super-Klein tunneling arises naturally as a direct consequence of the intrinsic connection of the model to free-particle dynamics, a relation that is established through methods of supersymmetric quantum mechanics, which provide an elegant and analytically tractable framework. Besides the mentioned super-Klein tunneling, scale invariance of the model and invisibility of the potential for particles of specific energy are revealed, and possible routes toward experimental realization are discussed.

A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.

Cascaded emission from the biexciton state of a quantum dot results in polarization entangled photon pairs. Cavity-enhancement of the direct two-photon emission channel bypasses the dominant source of decoherence in this system - that due to fine-structure splitting of the exciton levels. Here, we investigate the remaining non-Markovian phonon-induced decoherence using the numerically exact uniTEMPO algorithm. We compute the degree of entanglement of photon pairs generated by pulsed two-photon resonant excitation and find surprisingly good agreement between the numerically exact results and those calculated using the approximate polaron master equation method, permitting an efficient exploration of trends across system parameters.

The quantum theory of the electromagnetic field enables the description of multiphoton states exhibiting nonclassical statistical properties, often reflected in non-Gaussian phase-space distributions. While non-Gaussianity alone does not fully characterize quantum states, several classifications have been proposed to hierarchize non-Gaussian states according to physically or informationally relevant resources. Here, we provide a physical interpretation of non-Gaussianity and connect it to a computational perspective by showing how a prominent classification-the stellar rank-emerges as a limiting case of the roots of polynomials that univocally represent bosonic states defined with a quantized phase reference, namely the Majorana polynomials. A direct consequence of our results is a revised interpretation of both the stellar rank and non-Gaussianity itself: when superselection rules are properly taken into account, quadrature non-Gaussianity - and nonzero stellar rank - act as witnesses of particle entanglement, rather than being linked with photon addition to Gaussian states as previously assumed. In addition, we show that because the stellar rank depends on a specific choice of coherent states, its relation to computational resources and potential quantum advantage is inherently basis-dependent, being naturally tied to quadrature eigenstates as the computational basis. Motivated by this observation, we generalize the notion of stellar rank to arbitrary computational bases, thereby establishing it as a genuine witness of bosonic resources that may enable quantum advantage.

The Out-of-Time-Order Correlator (OTOC) is a standard algebraic diagnostic of quantum information scrambling, but it offers limited direct geometric intuition. In this note, we propose a Bohmian, trajectory-based framework for constructing a geometric diagnostic of scrambling-related sensitivity using Lagrangian Descriptors (LDs). To avoid the uncertainty-principle obstruction to assigning independent initial position and momentum within a single wave function, we evaluate Bohmian dynamics over a two-dimensional preparation space of localized Gaussian wavepackets labeled by their initial center and momentum kick. For the inverted harmonic oscillator, this construction is analytically tractable: the wavepacket-center dynamics and their dependence on preparation parameters can be written explicitly. In particular, away from the equilibrium origin, the exponential growth of the associated preparation-space stability matrix yields an $\mathcal{O}(e^{\omega T})$ bound on the sensitivity of the wavepacket-center LDs, motivating a semiclassical comparison with sensitivity structures associated with OTOC growth. In this sense, the LD provides a geometric indicator of scrambling-related sensitivity. We conclude by discussing how this preparation-space picture suggests a program for future work regarding the distinct microcanonical regimes previously reported for the inverted harmonic oscillator.

Collective dynamics in engineered quantum systems offer a unique and versatile platform for exploring how many-body correlations bridge microscopic entanglement and macroscopic behavior. In this work, we report collective Dicke dynamics of acoustic modes in a macroscopic high-overtone bulk acoustic resonator (HBAR). To achieve this, we engineer a hybrid quantum acoustodynamic system comprising an HBAR strongly coupled to a superconducting transmon qubit. The HBAR device is distinctive in the sense that its narrow mode spacing, together with enhanced qubit-mode coupling strength, gives rise to efficient coupling between the transmon and clusters of near-resonant modes. By harnessing the system properties, we observe collective dynamics involving clusters composed by two or three mechanical modes, where their non-resonant spectrum allows for the observation of the transition between the Dicke static regime to dynamically induced timed-Dicke one. The coherent collective behavior of the system is supported by time-domain measurements of the qubit's purity, indicating the quantum nature of the collective dynamics. Overall, our work establishes HBAR-based hybrid quantum system as a promising platform for exploring many-body collective dynamics in macroscopic mechanical systems.

Magic – the resource enabling quantum computational advantage beyond stabilizer circuits – has a clean phase-space characterization in odd prime dimensions that qubits notoriously lack. We study C(rho), the l_1 distance from a state's discrete Wigner function to the stabilizer polytope, and determine its exact geometry. For a single qubit with Bloch vector r we prove the closed form C = max(0, ||r||_1 - 1)/2, so the maximum is (sqrt(3)-1)/2, attained at the eight face states. For products of single-qubit states, C(rho_1 x ... x rho_n) <= prod_i (1 + C(rho_i)) - 1, with equality whenever every factor has Bloch sign product r_x r_y r_z <= 0; this includes the exact tensor powers ((1+sqrt(3))/2)^n - 1 and the exact maximum of C over fully separable n-qubit states. Because no discrete Wigner function for qubits is Clifford covariant, any such measure is frame dependent, and we identify which of its features are not. For a single qubit there are exactly two valid frames up to phase-space translation and C is identical on both. Pauli-covariant two-qubit frames number 2048 up to translation, and across them the ratio C(rho_Rx)/C(rho_Ry) takes the values 1/2, 1 and 2. In every one of these frames some stabilizer state has negative Wigner entries, a consequence of the Mermin-Peres square, so the two-qubit bound Gamma >= 1 + C/2 against the robustness of magic Gamma is frame independent. Within the Wootters frame we prove integer values 1, 2, 1 of the tightness ratio kappa := (Gamma-1)/C for three families in the two-qubit repetition codespace, with explicit certificates. For n-qubit GHZ phase states we prove Gamma = |sin phi| + |cos phi| for all n and C >= 2^(floor(n/2)-1) (|sin phi| + |cos phi| - 1), tight for n = 2 and, by exact linear programming, for n = 3, 4, so kappa decays exponentially. Finally, C is not a magic monotone, so it cannot replace Gamma in distillation bounds.

In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement.

The state overlap, quantified via $\tr[\rho \sigma]$, is a metric widely used to assess the closeness between two quantum states $\rho$ and $\sigma$. Although global state overlap alone does not directly capture entanglement properties, we uncover that incorporating local state overlaps provide profound insights into the entanglement characteristics of quantum states. To be precise, the ratio of global to local state overlaps provides a lower bound on the Schmidt number, which is usually used for quantifying high-dimensional entanglement. Unlike conventional methods for detecting entanglement, the approach here can simultaneously reveal entanglement information for two unknown quantum states. Moreover, state overlap can be efficiently determined through local randomized measurement methods, which ensures the experimental feasibility of our approach. In a special case, our criterion reduces to an entanglement criterion that is more powerful than the two criteria used most in experiment–the purity criterion and the fidelity-based criterion and also outperform the $p_3$-PPT method in specific instances. Our findings highlight a promising direction for advancements in entanglement detection experiments.

In this paper I propose a branch point twist field approach to computing the temporal entropy, that is, an entanglement measure across different time regions, as opposed to the usual spacial measures. Considering only the ground state of a gapped theory, I discuss how the shift to time-dependence manifests in form factor calculations. I show that the generalization of the spacial measures to temporal ones reproduces expected features of the temporal entanglement: the entropy is complex, oscillatory and reminiscent of the evolution of entanglement following a global quench. Considering the temporal von Neumann entropy, I argue that spacial and temporal entropies are two sides of the same coin. They both encapsulate universal information about the theory, in particular its mass spectrum. Also in both cases, a quasiparticle picture can be employed to interpret results. This picture connects features of the temporal entropy with those of the spacial entropy following a quantum quench.

We show that, for a one - dimensional open quantum system of ultracold atoms trapped in an array of harmonic potentials that is weakly coupled to a background Bose - Einstein Condensate (BEC), a unique steady state emerges at either of the two edges of the array due to the combined effects of excitation via lasers of these ultracold atoms and decay back to their initial energy levels via emission of excitations into the BEC, acting as an excitation reservoir. We then demonstrate the existence of steady states of the master equation that describes the dynamics of this open quantum system with respect to the expectation value of the position of the harmonic potential containing these states, and show that these steady states occur at the edges of the array of harmonic potentials trapping these atoms. Using the open quantum system's master equation to evolve initial states of the system that are trapped in other harmonic potentials in the array numerically over time, we verify the analytic calculations demonstrating the existence of these steady states at the edge of the system, and further demonstrate that these steady states will emerge regardless of the number of atoms trapped in each of the harmonic potentials in the array. We note that the emergence of these edge states irrespective of the initial state of the system is similar to the non-Hermitian skin effect seen in other open quantum systems, and are of fundamental importance in quantum technological applications such as quantum transport and quantum batteries.

In this paper we investigate the asymptotic statistical theory of irreducible quantum Markov chains, focusing on identifiability properties and asymptotic convergence of associated quantum statistical models. We show that the space of identifiable parameters for the stationary output is a stratified space called an orbifold, which is obtained as the quotient of the manifold of irreducible dynamics by a compact group of state preserving symmetries. We analyse the orbifold's geometric properties, the connection between periodicity and strata, and provide orbifold charts as the starting point for the local asymptotic theory. The quantum Fisher information rate of the system and output state is expressed in terms of a canonical inner product on the identifiable tangent space. We then show that the joint system and output model satisfies quantum local asymptotic normality while the stationary output model converges to a product between a quantum Gaussian shift model and a mixture of quantum Gaussian shift models, reflecting the underlying periodicity. These strong convergence results provide the basis for constructing asymptotically optimal estimators of dynamical parameters. We provide an in-depth analysis of the model with smallest dimensions, consisting of two-dimensional system and environment units.

We report the realization of multilayer three-dimensional nanobridge Josephson junctions based on Nb/NbN and Nb/TiN superconducting stacks fabricated using electron-beam lithography and chlorine-based dry etching. In this architecture, a high-resistivity nitride layer defines the geometrical weak link, while the top Nb layer sets the overall critical temperature and film quality of the stack. This multilayer design enables engineering of the superconducting gap and proximity effects without relying on focused ion beam milling or oxide tunnel barriers. The devices are successfully integrated into dc SQUIDs, demonstrating reliable circuit-level operation. By combining material selectivity with three-dimensional geometry, this platform provides a scalable route toward oxide-free Josephson junctions suitable for superconducting electronics.

Prior to this work, the largest known gap between the entangled value and the classical value for a one-round two-player nonlocal game with a perfect entangled strategy using two Bell states of entanglement was $\frac{1}{9}$, achieved by the Mermin-Peres magic square game. A larger gap of $\frac{2}{15}$ has been claimed for the related doily game of Kelleher, Roomy, and Holweck (Quant. Inf. Proc., 2024). However, this value assumes that the classical players use identical local strategies, and we show that dropping this assumption reduces the gap back to $\frac{1}{9}$. We then demonstrate that $\frac{1}{9}$ is not optimal by explicitly constructing a new nonlocal game with gap $\frac{4}{35}$.

We propose a frequency-division multiplexed (FDM) continuous-variable quantum key distribution (CV-QKD) system with enhanced spectral efficiency through optimized channel spacing of low-symbol-rate signals. A four-channel 10-Mbaud FDM-CV-QKD system was experimentally demonstrated using Gaussian modulation, a transmitted local oscillator, and homodyne detection. Despite the inter-channel interference, under a finite-size scenario (m=1.25x10^6), the system achieved a 3.6-fold back-to-back secret key rate gain and outperformed the single-channel frequency-upconverted signal up to 26.8 km.

Whether the sets of absolutely separable (AS) and absolutely two-qutrit positive-partial-transpose (AP) states are the same has been an open problem in entanglement theory for decades. Since they are both convex sets, we investigate the boundary and extreme points of full-rank two-qutrit AP states with exactly three distinct eigenvalues. We show that every boundary point is an extreme point, with exactly one exception. We explicitly characterize the expressions of such points, each of which turns out to contain at most one parameter in some intervals. When the parameter approaches the ends of intervals, most points become the known extreme points of exactly two distinct eigenvalues. We present our results by tables and figures.

The quantum corrections to the behavior of a semi-classical gas can be expressed as a power series of the ratio $eta$ between the cube of De Broglie's thermal wavelength and the specific volume. The connection between $eta$ and the multioccupancy of quantum states is the aim of the present work. By means of a chemical/physical approach it is possible to associate $eta$ to the concrete realization of multioccupancy in momentum space, through the formation of what we call "pseudo-molecules", i.e. multiplets of particles sharing momenta whose differences are negligeable in the continuous spctrum approximation. The pseudo-molecules result as casual consequences of multiple scattering processes among non interacting (scattering apart) particles.

Finding the minimum spanning tree (MST) of a graph is an important task in computer vision, as it enables a sparse and low-cost representation of connectivity among elements (such as superpixels, points, or regions), which is useful for tasks such as segmentation, reconstruction, and clustering. In this work, we propose and evaluate a fully quantum pipeline for computing MSTs using the FALQON algorithm, a feedback-based quantum optimization method that does not require classical optimizers. We construct a Hamiltonian formulation whose ground-state energy encodes the MST of a graph and compare different FALQON strategies: (i) time rescaling (TR-FALQON) and (ii) multi-driver configurations. To avoid domain-specific biases, we adopt graphs with random weights and show that the FALQON variants exhibit significant differences in ground-state fidelity. We discuss the relevance of this approach for computer vision problems that naturally yield graph representations, and experimental results on synthetic instances together with a small demonstrative study on image segmentation illustrate both the potential and the current limitations of the method. Our numerical simulations on randomly weighted graphs show that standard one drive FALQON, although it reduces the expected energy, fails to concentrate amplitude in the MST solution. The multi drive variant succeeds in redistributing probability mass toward the ground state so that the MST appears among the most probable outcomes, and TR FALQON applied over multi drive produces the best results with faster convergence, lower final energy, and the highest solution state probability or fidelity in our tested instances. These improvements were observed on small synthetic graphs, underscoring both the promise of multi drive controls with temporal rescaling and the need for further scaling and hardware validation.

The scalability of quantum computing in supporting sophisticated algorithms critically depends not only on qubit quality and error handling, but also on the efficiency of classical control, constrained by the cryogenic control bandwidth and energy budget. In this work, we address this challenge by investigating the algorithmic complexity of quantum circuits at the instruction set architecture (ISA) level. We introduce an energy-efficient quantum instruction set architecture (EQISA) that synthesizes quantum circuits in a discrete Solovay-Kitaev basis of fixed depth and encodes instruction streams using a sparse dictionary learned from decomposing a set of Haar-random unitaries, followed by entropy-optimal Huffman coding and an additional lossless bzip2 compression stage. This approach is evaluated on benchmark quantum circuits demonstrating over 60% compression of quantum instruction streams across system sizes, enabling proportional reductions in classical control energy and communication overhead without loss of computational fidelity. Beyond compression, EQISA facilitates the discovery of higher-level composable abstractions in quantum circuits and provides estimates of quantum algorithmic complexity. These findings position EQISA as an impactful direction for improving the energy efficiency and scalability of quantum control architectures.

Non-Hermitian systems have emerged as a powerful paradigm for ultrasensitive sensing, leveraging unique spectral and dynamical properties unmatched in Hermitian physics. While recent theoretical bounds suggest these protocols offer no metrological advantage over Hermitian ones in the ideal shot-noise-limited regime when rigorously accounting for the success probability of non-unitary evolution, their practical utility in realistic experimental conditions has not yet been systematically explored. In this work, we shift the focus toward practical laboratory performance and demonstrate that non-Hermitian sensing protocols can significantly outperform their Hermitian counterparts in the presence of pervasive classical technical noises. This performance gain mainly stems from a strongly enhanced susceptibility that amplifies the signal response, effectively overcoming the precision floor imposed by technical imperfections. By numerically evaluating the Fisher information under technical noise, we further substantiate the regimes where non-Hermitian platforms yield definitive practical gains. Our results reconcile the ongoing debate between fundamental limits and experimental observations, offering a concrete avenue for building high-precision, noise-resilient sensors.

We introduce a Lindblad-deformed spectral geometric framework in which bounded dissipative data deform a standard spectral triple through the Dirac operator D_gamma = D - igammaSigma, where Sigma = (1/2) sum_k L_k^dagger L_k is constructed from Lindblad jump operators {L_k}. The associated positive operator Q_gamma = D_gamma^* D_gamma = D^2 + gamma^2 Sigma^2 - i*gamma [D, Sigma] is identified as the correct spectral-geometric observable. For smooth endomorphism-valued Lindblad data, Q_gamma is of Laplace type and admits a standard heat-kernel asymptotic expansion with dissipation-modified even Seeley-DeWitt coefficients. For the scalar deformation L = sqrt(gamma) f with f in C^infty(M) real-valued, we prove that the first-order Duhamel correction to the heat trace K_gamma(sigma) = Tr(exp(-sigma Q_gamma)) vanishes identically, so that the first nontrivial dissipative effect appears at order gamma^4. We identify the exact Duhamel-level decomposition of the O(gamma^4) correction into a direct W_2 insertion and a quadratic W_1 x W_1 term. In the round S^2 model we determine the explicit deformed operator and extract the leading local asymptotic contribution of the W_2 sector. We define the effective scale-dependent spectral dimension d_{s,eff}(sigma,gamma) = -2 d/d(log sigma) log K_gamma(sigma) and identify its leading perturbative deformation.

The development of many scalable quantum technologies requires single-photon nonlinearity, such as single-photon blockade, in solid-state systems. Recently, it has been shown that single-photon Fock states can, in principle, be unconditionally generated using arbitrarily small intrinsic optical nonlinearities in photonic cavities. We investigate the feasibility of such a scheme in achieving photon blockade in an on-chip silicon photonics platform. We show that a triply resonant nanobeam cavity pumped with three monochromatic lasers could achieve such functionalities with quality factors $\sim 10^7$ and effective mode volumes $\sim 10^{-2} \mu m^3$, for experimentally feasible incident powers. Using quantum optical simulations, we propose an experimental protocol to generate single photons under this scheme. The constraints on the cavity design and experimental conditions are thoroughly explored to determine feasible regimes of operation.

We point out that, when an optimization problem has more than one solution, the quantum adiabatic algorithms (QAA) encounter topological obstructions leading to adiabatic spectral flows where spectral branches unavoidably traverse the spectral gap above the ground states of the quantum Hamiltonians. This raises serious doubts about the validity of the algorithms in such situations. However, using the Max-Cut problem as an example, we explain and demonstrate here that QAAs correctly detect all existing solutions in one single run. This newly discovered capacity of QAAs to simultaneously detect multiple solutions to an optimization problem can have an important impact on future developments of quantum variational algorithms

Scalable quantum characterization and error-mitigation workflows often rely on the assumption that relevant device noise and readout contamination can be adequately captured by low-weight, predominantly pairwise interactions. We report a compact hardware experiment designed to operationally distinguish pairwise-only explanations from irreducible triplet-order predictive structure. The A1/A1b protocol implements a parity-structured binary label on a 133-qubit IBM superconducting processor (ibm_torino) and analyzes the resulting data through a classical M"obius decomposition of subset mutual informations. In the A1 baseline, we observe a macroscopic triplet correlation of f(123) = 0.72609 bits (p <= 1.0e-4, permutation floor). In the strict A1b loophole-reduction follow-up, role-symmetry averaging sharply suppresses singleton leakage, modestly reduces pairwise mismatch, and preserves a large irreducible triplet term of f(123) = 0.56521 bits. Crucially, a principled pairwise maximum-entropy baseline consistent with the empirical 1- and 2-body marginals implies only f(123) ~ 6.6e-6 bits, in strong contradiction with the observed hardware data. On A1b, a classifier built exclusively from pairwise features reaches only 0.617 held-out accuracy (chance 0.5), whereas a triplet-inclusive model reaches 0.910. These results provide a concise, open-data demonstration that pairwise benchmarking proxies can be fundamentally blind to higher-order contextual structure in present-day superconducting experiments.

In classical systems, chaos is clearly defined via the behavior of trajectories. In quantum systems with a classical analogue one finds that the transition from regular to chaotic dynamics is signified by a change in the spectral statistics. This has been found to remain true for quantum systems with no classical analogue, including many-body systems. Furthermore, quantum chaotic systems explore all the allowed configurations in the Hilbert space, i.e. they are ergodic, while integrable systems, and systems in the many-body localized phase, are restricted to a certain subspace of the available phase space, and hence strongly break ergodicity. In this dissertation, we study the intermediate behavior between ergodicity and localization, i.e. the weak breaking of ergodicity. The model examined is the PXP spin chain model, where spins are allowed to flip only under certain kinetic constraints. We start by reproducing some already established results. First, we explore the eigenstate thermalization hypothesis (ETH) for this model and demonstrate the existence of a small number of states, throughout the PXP spectrum, that violate the ETH. Then we study the level-spacing statistics of the model, a well-known quantum chaos diagnostic, which turns out to be close to semi-Poisson and approach Wigner–Dyson statistics for large system sizes. Moreover, we examine various aspects of the model that have not been studied before. For example, the eigenvector component statistics, another quantum chaos diagnostic, for the PXP model turn out to be non-Gaussian. Finally, we perform a quench, in order to study how the energy spreads throughout the system, and observe ballistic fronts.

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can closely emulate states of composite quantum systems, such as coupled two-level systems that display separable linear combinations of states. Examples of classical systems are suggested that show these states. These include multipole moments of waves or networks of phase oscillators. The work indicates that composite QL states can be manifest in complex network structures relevant to quantum biology or engineered into circuits, or even possibly soft matter.

Quantum nonlinearity is an essential ingredient for many quantum technologies, but often the nonlinearity is too weak to be exploited at the few-photon level. However, few photons interacting strongly with single quantum emitters in a waveguide environment can impact a significant nonlinear response, opening up a wide range of photon-photon correlations. Using a waveguide-QED system containing a single atom (treated as a two-level system) chirally coupled to a waveguide, we theoretically investigate two-photon nonlinearities with delay-controlled temporal correlations. We use both matrix product states (MPS) and a frequency-dependent scattering theory approach to analyze the exact population dynamics, as well as the first-order and second-order photon correlation functions in transmission of the system, when pumped by a two-photon Fock-state pulse with a bimodal temporal pulse envelope. The two-photon Fock-state pulses are considered to be either two single photons localized to each peak of the pulse, or both photons delocalized (but correlated) between the two peaks. We consider the regimes of a short, moderate, and (relatively) long distance between the two pulse peaks, comparing the important differences in the temporal correlations with the two types of two-photon pulses. We demonstrate the strikingly different nonlinear features and quantum correlations that occur for uncorrelated and correlated two-photon pairs in experimentally accessible regimes.

A long chain of Bose condensates freely expands and interferes after being released from an optical lattice. The interference fringes are well resolved both in the case of equal phases of the condensates and in the case of fluctuating phases. In the second case the positions of the fringes also fluctuate. The spectrum of the spatial density distribution, however, is reproducible despite the fluctuations. Moreover two types of peaks are distinguishable in the spectrum. The first type arises due to the phase fluctuations, the second type is associated with the coherence between the condensates. In the framework of the Pitaevskii-Gross equation we calculate the interference of the condensates and compare the calculation with experiment [Phys. Rev. Lett. 122, 090403 (2019)]. The calculation reproduces the positions of the spectrum peaks, including the dependence on the interparticle interaction. The calculated heights of the peaks, however, in some cases differ with the experimental ones.

For a long periodic chain of Bose condensates prepared in the free space, the subsequent evolution and interference dramatically depend on the difference between the phases of the adjacent and more distant condensates. If the phases are equal, the initial periodic density distribution reappears at later times, which is known as the Talbot effect. For randomly-related phases, we have found that a spatial order also appears in the interference, while the evolution of the fringes differs with the Talbot effect qualitatively. Even a small phase disorder is sufficient for qualitatively altering the interference, though maybe at long evolution times. This effect may be used for measuring the amount of coherence between adjacent condensates and the correlation length along the chain.

For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to non-zero) their zero-error capacity. In contrast, we show that for classical point-to-point channels with causal CSIT (channel state information at the transmitter), quantum entanglement assistance can in some cases improve their capacity, and in some cases activate their zero-error capacity.