We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand support a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities for the hypothesis. In model-dimension certification tasks, we show that the relative-belief procedure typically chooses Hilbert spaces that are never smaller in dimension than those selected from optimizing a broad class of information criteria, including Akaike's criterion. As a concrete and focused exposition of this powerful evidence-based technique, we apply the relative-belief procedure to an important application: state reconstruction of imperfect quantum sources. In particular, just by comparing prior and posterior probabilities based on data, we demonstrate its capability of tracking multiphoton emissions using (realistically lossy) single-photon detectors in order to assess the actual quality of photon sources without making ad hoc assumptions, thereby reliably safeguarding source integrity for general quantum-information and communication tasks with Bayesian reasoning. Finally, we discuss how relative belief can be exploited to carry out parametric model certification and estimate the total dimension of the quantum state for the combined (measured) physical and interacting external systems described by the Tavis-Cummings model.

Computational power in measurement-based quantum computing stems from the symmetry-protected topological (SPT) order of entangled resource states. However, resource states are prone to preparation errors. We introduce a quantum error correction approach using redundant nonlocal symmetry of the resource state. We demonstrate it within a teleportation protocol based on extending the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry of one-dimensional cluster states to other graph states. Qubit ZZ-crosstalk errors, which are prominent in quantum devices, degrade the teleportation fidelity of the usual cluster state. However, as we demonstrate on quantum hardware, once we grow graph states with redundant symmetry, perfect teleportation fidelity is restored. We identify the underlying redundant-SPT order as error-protected degeneracies in the entanglement spectrum.

The quantum speed limit (QSL) is the lower bound on the time required for a state to evolve to a desired final state under a given Hamiltonian evolution. Three well-known QSLs exist: the Mandelstam-Tamm (MT), Margolus-Levitin (ML), and dual ML (ML*) bounds. We consider one-dimensional systems that undergo a delocalization-localization transition in the presence of quasiperiodic and linear potential. By performing sudden quenches across the phase boundary, we find that the exact dynamics gets captured very well by QSLs. We show that the MT bound is always tighter in the short-time limit for any arbitrary state, while the optimal bound for the time of orthogonalization (time required to reach the orthogonal state) depends on the choice of the initial state. Further, for extreme quenches, we prove that the MT bound remains tighter for the time of orthogonalization and it can qualitatively describe the nonanalyticity in free energy for the dynamical quantum phase transition. We also demonstrate that the localization-delocalization transition point can be exactly identified from QSLs for two of the models of noninteracting fermions. Further, we also show that even for interacting systems, an ergodic to many-body localization transition can also be efficiently predicted from QSLs, whose computation cost is much less than other diagnostic tools.

Quantum distillation is a modern technology to decrease the von Neumann entropy of a subsystem by coherent system dynamics. Here we propose an active quantum distillation protocol, in which a bang-bang theme is applied to actively control the coherent dynamics of our system in order to obtain a subsystem with the von Neumann entropy as low as possible. For a bipartite bosonic system, we derive the analytical expression of the entropy lower bound of one subsystem under any unitary transformation for mixed states with conservation of particles. The lower bound is validated by numerical simulations on the Bose-Hubbard model, where the coherent evolution is controlled by tuning one interaction term of the Hamiltonian. Our protocol can be used to decrease the entropy of one subsystem lower than the total bipartite state and increase the number of bosons or only distill out very few bosons in the subsystem.

Quantum vortices with more than a single circulation quantum are usually unstable and decay into clusters of smaller vortices. One way to prevent the decay is to place the vortex at the center of a convergent (draining) fluid flow, which tends to force vortices together. It is found that while the primary splitting instability is suppressed in this way (and completely quenched for strong enough flows) a secondary instability can emerge in circular trapping geometries. This behavior is related to an instability of rotating black holes when superradiantly amplified waves are confined inside a reflective cavity. The end state of the secondary instability is dramatic, manifesting as a shock wave that propagates round the circular wall and nucleates many more vortices.

We consider an impurity in a sea of zero-temperature fermions uniformly distributed throughout the space. The impurity scatters on fermions. On average, the momentum of impurity decreases with time as $t^{-1/(d+1)}$ in $d$ dimensions, and the momentum distribution acquires a scaling form in the long-time limit. We solve the Lorentz-Boltzmann equation for the scaled momentum distribution of the impurity in three dimensions. The solution is a combination of confluent hypergeometric functions. In two spatial dimensions, the Lorentz-Boltzmann equation is analytically intractable, so we merely extract a few exact predictions about asymptotic behaviors when the scaled momentum of the impurity is small or large.

Estimation of the phase delay between interferometer arms is the core of transmission phase microscopy. Such phase estimation may exhibit an error below the standard quantum (shot-noise) limit, if the input is an entangled two-mode state, e.g., a N00N state. We show, by contrast, that such supersensitive phase estimation (SSPE) is achievable by incoherent, e.g., thermal, light that is injected into a Mach-Zehnder interferometer via a Kerr-nonlinear two-mode coupler. Phase error is shown to be reduced below $1/\overline{n}, \overline{n}$ being the mean photon number, by thermal input in such interferometric setups, even for small nonlinear phase shifts per photon pair or for significant photon loss. Remarkably, the phase accuracy achievable in such setups by thermal input surpasses that of coherent light with the same $\overline{n}$. Available mode couplers with giant Kerr nonlinearity that stem either from dipole-dipole interactions of Rydberg polaritons in a cold atomic gas, or from cavity-enhanced dispersive atom-field interactions, may exploit such effects to substantially advance interferometric phase microscopy using incoherent, faint light sources.

We present a cryptographic-inspired framework for modeling Bell nonlocal correlations. Drawing inspiration from the renowned de Broglie–Bohm theory, we conceptualize nonlocal boxes as realistic systems featuring instantaneous signaling at the hidden-variable level. By introducing randomness into the distribution of the hidden variable, the superluminal signaling model is made compatible with the operational no-signaling condition. As our design mimics the famous symmetric key encryption system called the one-time pad (OTP), we call this the OTP model for nonlocal boxes. We illustrate the efficacy of this model through various esoteric examples related to the nonclassical nature of nonlocal boxes. In particular, the breakdown of communication complexity using nonlocal boxes can be better understood in this framework. Additionally, we delve into the Van Dam protocol, revealing its connection to homomorphic encryption studied in cryptography. Exploring potential avenues for encapsulating quantum-realizable nonlocal correlations within our framework, we highlight that the information causality principle imposes additional constraints at the hidden-variable level. Present work thus orchestrates the results in classical cryptography to improve our understanding of nonlocal correlations and welcomes further research to this connection.

We study theoretically two consequences of the mixed classical phase space for three repulsively interacting bosonic particles in a circular trap. First, we show that the energy levels of the corresponding quantum system are well described by a Berry-Robnik distribution. Second, we identify stationary quantum states whose density is enhanced along the stable classical periodic trajectories, and calculate their energies and wave functions using the semiclassical Einstein-Brillouin-Keller (EBK) theory. Our EBK results are in excellent agreement with our full-fledged finite-element numerics. We discuss the impact of discrete symmetries, including bosonic exchange symmetry, on these classically localized states. They are within experimental reach, and occur in the same range of energies as the quantum scar reported in our previous work [Phys. Rev. A 107, 022217 (2023)].

We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modeling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth by Van Herstraeten and Cerf [Phys. Rev. A 104, 042211 (2021)] and Hertz et al. [J. Phys. A: Math. Theor. 50, 385301 (2017)]. Said conjecture asserts that the differential entropy defined for non-negative, yet physical, Wigner functions is minimized by pure Gaussian states while the minimum entropy is equal to $1+ln\pi$. We prove this conjecture for the qubits formed by Fock states $|0\rangle$ and $|1\rangle$ that correspond to non-negative Wigner functions. In particular, we derive an explicit form of the Wigner entropy for those states lying on the boundary of the set of Wigner non-negative qubits. We then consider general mixed states and derive a sufficient condition for the conjecture's validity. Lastly, we elaborate on the states which are in accordance with our condition.

We study the energy-transfer process in the recently proposed sunburst quantum Ising model, which consists of two interacting integrable systems: a transverse Ising chain with a very small transverse field and a finite number of external isolated qubits. We show that in this model of the quantum battery, coupling between the battery and charger can be used to optimize the ergotropy, which is the maximum amount of energy that can be extracted from the battery. At the same time, maximum charging power increases with the coupling strength, allowing for the simultaneous optimization of both ergotropy and charging power in the strong-coupling limit. Furthermore, we show that both ergotropy and charging power are independent of the initial state of the charger.

Quantum sensor networks have often been studied in order to determine how accurately they can determine a parameter, such as the strength of a magnetic field, at one of the detectors. A more coarse-grained approach is to try to simply determine whether a detector has interacted with a signal or not, and which detector it was. Such discrete-outcome quantum sensor networks, discrete in the sense that we are seeking answers to yes-no questions, are what we study here. One issue is what is a good initial state for the network, and, in particular, should it be entangled or not. Earlier we looked at the case when only one detector interacted, and here we extend that study in two ways. First, we allow more than one detector to interact, and second, we examine the effect of grouping the detectors. When the detectors are grouped we are only interested in which group contained interacting detectors and not in which individual detectors within a group interacted. We find that in the case of grouping detectors, entangled initial states can be helpful.

We find that a quantum device having an accessory involving precision measurement can have an enhancement of its metrological precision in estimating an unknown parameter of the quantum system by insertion of glassy disorder, accidental or engineered. We clearly mention how an unbiased estimator can also be identified in a disordered situation and how the precision thereof can be bounded by the quantum Crámer-Rao inequality. We compare the Fisher information-based lower bound of the minimum standard deviation of an unbiased estimator, in the presence of glassy disorder in the system, with the same of an ideal, viz. disorder-free, situation. The phenomenon can boost the efficiency of certain measuring devices, such as atomic clocks. The precision of these clocks, when measuring time, hinges on the precise determination of the frequency of a two-level atom. In cases where impurities are present in the atom, and can be modeled as a disorder parameter, it is possible for the measurement of frequency to be more accurate than in an ideal, disorder-free scenario. Moreover, disorder insertion can reduce the requirement of entanglement content of the initial probes, which are copies of two-qubit states, along with providing a disorder-induced enhancement.

This paper discusses the possibility of using two-mode squeezed light to improve the performance of existing sensor technology with the focus on its miniaturization under realistic losses. Therefore, we analyze a system consisting of a part for two-mode squeezed light generation, a sensor region, and a detection stage. Based on a general four-wave mixing (FWM) Hamiltonian caused by third-order susceptibility, we formulate linearized equations that describe the FWM process below the threshold and are used to analyze the squeezing quality of the generated optical signal and idler modes. For a possible realization, the focus is set on chip-integrated generation using microring resonators. To do so, the impacts of the design and the pump light are considered in the derived equations. These equations are used to analyze the usage of two-mode squeezed light in quantum metrology and the application in a Mach-Zehnder interferometer. Due to the impact of losses in realistic use cases, we show that the main usage is for small and compact devices, which can lead to a quantum improvement of up to a factor of 10 in comparison with using coherent light only. This enables the use of small squeezing-enhanced sensors with a performance comparable to larger classical sensors.

Standard perturbation theory in quantum mechanics is employed to calculate the mass shifts of $2{}^{1}S_0-2{}^{3}S_1$ and $2{}^{3}S_1-2{}^{3}P_J$ transitions in ${}^{7,9,10,11,12,14}\mathrm{Be}^{2+}$ ions. These mass shifts are determined with high precision, typically having uncertainties of 1–2 ppm. The sensitivity of the isotope shifts between ${}^{7,10,11,12,14}\mathrm{Be}^{2+}$ and ${}^9\mathrm{Be}^{2+}$ to differences in nuclear charge radii is examined. Moreover, we present the fine-structure splitting isotope shifts, which serve as valuable tools for testing the consistency of experimental results. The study presented here will provide valuable insights for future measurements aimed at extracting atomic physics values of Be nuclear charge radii differences with an accuracy of 5% or higher.

Heralding, which is often used for preparing quantum optical states, is studied to determine the effects of the spatiotemporal properties of the process. Incorporating all the spatiotemporal degrees of freedom, we follow a Wigner functional approach to consider cases where these states are prepared to have Wigner functionals with negative regions, being suitable resources for quantum information technologies. General expressions are derived for single-photon-subtracted and single-photon-added states. As examples, we consider the photon-subtracted squeezed vacuum state, the photon-added coherent state, the photon-added thermal state, and the photon-added squeezed vacuum state. The Wigner functional approach reveals the importance of the spatiotemporal transformations imposed by the experimental conditions.