An entangled state is said to be $m$-uniform if the reduced density matrix of any $m$ qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow us not only to correct errors but also to identify their precise nature and location. Here, we show how to create $m$-uniform states using local gates or interactions and elucidate several QECC applications. We first show that $D$-dimensional cluster states are $m$-uniform with $m=2D$. This zero-correlation-length cluster state does not have finite-size corrections to its $m=2D$ uniformity, which is exact both for infinite lattices and for large enough, but finite, lattices. Yet at some finite value of the lattice extension in each of the $D$ dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger $m$ values using quasi-$D$-dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the one-dimensional cluster state, which, as we show, allows us to detect and identify one-qubit errors, distinguishing $X, Y$, and $Z$ errors.

Electronic excited states of molecules are central to many physical and chemical processes, and yet they are typically more difficult to compute than ground states. In this paper we leverage the advantages of quantum computers to develop an algorithm for the highly accurate calculation of excited states. We solve a contracted Schrödinger equation (CSE)—a contraction (projection) of the Schrödinger equation onto the space of two electrons—whose solutions correspond identically to the ground and excited states of the Schrödinger equation. While recent quantum algorithms for solving the CSE, known as contracted quantum eigensolvers (CQEs), have focused on ground states, we develop a CQE based on the variance that is designed to optimize rapidly to a ground or excited state. We apply the algorithm to compute the ground and excited states of ${\mathrm{H}}_2, {\mathrm{H}}_4$, and BH.

We study the vortex nucleation dynamics in inhomogeneous atomic Bose gases quenched into a superfluid phase and investigate the dependence of the Kibble-Zurek (KZ) scaling exponent on the underlying trap configuration. For samples in a number of different inhomogeneous traps, we observe the characteristic power-law scaling of the vortex number with the thermal quench rate, as well as an enhanced vortex suppression in the outer regions with lower particle density, in agreement with the causality effect as encapsulated in the inhomogeneous Kibble-Zurek mechanism (IKZM). However, the measured KZ scaling exponents show significant differences from the theoretical estimates, and furthermore their trends as a function of the underlying trap configuration deviate from the IKZM prediction. We also investigate the early-time coarsening effect using a two-step quench protocol as proposed in a recent study and show that the interpretation of the measurement results without including the causality effect might be misleading. This paper provides a comprehensive study of vortex formation dynamics in quenched Bose gases confined in inhomogeneous trapping potentials and calls for a refined theoretical framework for quantitative understanding of the phase transition and defect formation processes in such inhomogeneous systems.

High-order harmonic generation (HHG) is one of the most commonly studied nonlinear optical phenomena, originating in the ultrafast dynamics of electrons in atomic gases and semiconductors. It has attracted much attention because of its nonperturbative nature and potential for future attosecond laser pulse sources. On the theory side, a semiclassical picture based on tunneling ionization of electrons is successfully used in explaining key characteristics of the HHG. This model assumes that electric fields nonperturbatively excite electrons beyond the ionization potential or the band gap. Thus, intuitively, a larger gap should lead to an exponentially smaller HHG emission. Despite this intuition, the HHG in the Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ has shown an unconventional exponential increase with respect to the gap width. This experiment implies effects beyond the semiclassical theory. However, most theoretical works have focused on the dependence of the HHG on external control parameters, and the gap dependence of the HHG is poorly understood even in noninteracting systems. Thus, it is essential to clarify the gap dependence of the HHG in a fully quantum mechanical approach. Here, we analyze numerically exactly the gap dependence of the HHG in two-level systems. We find an increase in the strength of the HHG when the Rabi frequency is large compared to the gap width. Furthermore, the relaxation and scattering of electrons increase the visibility of this gap dependence. Finally, we find that the enhancement rate follows a universal scaling law regardless of the driving frequency. The existence of this gap dependence in two-level systems suggests that this unconventional gap dependence is a universal behavior that can be found not only in Mott insulators but also in atomic gases and semiconductors.

When loss is introduced in one arm of a pair of coupled waveguides, it can result in an output signal with increased spatial coherence compared to the input beam. To theoretically investigate this phenomenon, we employ the formalism of classical coherence theory and develop a continuous model for the waveguides, treating them as a pair of Gaussian profiles. Our study focuses on the dynamics of the cross-spectral density function and the effective degree of coherence.

Vacuum-induced coupling (VIC), arising from the quantum interference between the spontaneous emission pathways from the excited doublet to a common ground state, has attracted significant research interest and has been observed in recent experiments. Here, we present an alternative route to probe the existence of VIC by means of the coherence statistics of photon antibunching and show that, under realistic experimental conditions, the vacuum-induced quantum beat (VIQB) can enable strong photon antibunching with high brightness in an optical nanofiber (ONF) cavity quantum electrodynamics (CQED) system. We find that the occurrence of the photon antibunching corresponds to the existence of the VIC, indicating that the photon antibunching can be an important witness for VIC. In addition, a strong photon antibunching effect appears in the weak-coupling regime of light-atom interactions when the VIQB is present, as a result of the destructive quantum interference between the different paths for two-photon excitation. Furthermore, we find that strong photon antibunching can be generated within a certain driving frequency range in the present system, which can relax the requirement for the driving frequency in the ONF CQED system. Also, we compare the analytical and numerical results of the second-order intensity correlation function, and they are in good agreement. The present study builds a bridge between the photon antibunching and the VIC and VIQB, which is useful for well understanding and researching a tunable single-photon source, as well as enabling potential applications in quantum information processing and quantum communications.

We experimentally demonstrate protective measurements by weakly coupling the polarization of a single-photon-level field to a measurement pointer that corresponds to the arrival time of the photon. By using an optical loop, we implement a variable, controlled number (1–9) of protection and measurement stages. We demonstrate the measurement of expectation values of photon polarization by measuring arrival times while simultaneously protecting the polarization state. No knowledge of the initial photon state is required or available in our experiment, demonstrating that protective measurements provide a genuine information gain that cannot simply be reduced to a priori information about the protection procedure.

We present several measurement schemes for accessing separability criteria for continuous-variable bipartite quantum systems. Starting from moments of the bosonic mode operators, criteria suitable to witness entanglement are expressed in terms of multimode spin observables via the Jordan-Schwinger map. These observables are typically defined over a few replicas of the state of interest and can be transformed into simple photon number measurements by passive optical circuits. Our measurement schemes require only a handful of measurements, thereby allowing one to efficiently detect entanglement without the need for costly state tomography as illustrated for a variety of physically relevant states (Gaussian, mixed Schrödinger cat, and NOON states). The influence of typical experimental imperfections is shown to be moderate.

We study the electron-positron pair-creation process under a combination of a temporally periodic and a spatially periodic field. In the short-time regime where the total yield of created pairs grows linearly, the creation rate due to the temporally oscillating field has been derived analytically. The creation process under a weak spatially periodic field is also found analytically by simplifying the model into sets of four-level systems. We find that the direct energy-conserving transition is negligible; there exist two competing paths that both require symmetric transitions when crossing the energy gap. In the long-time limit, the total creation yield grows in a damped oscillatory fashion and finally relaxes to a specific value as the Rabi oscillations of each four-level system dephase. Compared to the situation with only the temporally periodic field, the spatially inhomogeneous field can increase the production rate due to the opening of new vacuum decay channels.

In a neutral-atom quantum computer, the qubits are individual neutral atoms trapped in optical tweezers. Excitations to Rydberg states form the basis for the entanglement procedure that is at the basis of multiqubit quantum gates. However, these Rydberg atoms are often antitrapped, leading to decoherence and atom loss. In this work, we give a quantum-mechanical description of the antitrapping loss rates and determine the recapture probability after Rydberg excitation, distinguishing between having the laser traps turned on and off. We find that ample time ($\approx 30\mathrm{\mu }\mathrm{s}$, in a ${}^{88}\mathrm{Sr}$ system) is needed for the wave functions to expand out of the trap. Therefore, even with traps on, $\approx 100$% recapture probabilities can be expected for times in which significant entanglement operations between atoms can be performed. We find that for two-dimensional radial traps with bosonic ${}^{88}\mathrm{Sr}$ atoms, the time in which perfect recapture can be achieved is of the same order of magnitude for traps turned on and off.

The dynamics of two interacting quantum particles on a weakly disordered chain is investigated. Spatial quantum interference between them is characterized through the statistics of two-particle transition amplitudes, related to Hanbury Brown-Twiss correlations in optics. The fluctuation profile of the signal can discern whether the interacting parties are behaving like identical bosons, fermions, or distinguishable particles. An analog fully developed speckle regime displaying Rayleigh statistics is achieved for interacting bosons. Deviations toward long-tailed distributions echo quantum correlations akin to noninteracting identical particles. In the limit of strong interaction, two-particle bound states obey compound Rician distributions.

We present an analytical approach for the study of driven Dicke superradiance based on a Heisenberg-Langevin formulation. We calculate the steady-state fluctuations of both the atomic-spin and light-field operators. While the atoms become entangled below a critical drive, exhibiting spin squeezing, we show that the radiated light is in a classical-like coherent state whose amplitude and spectrum are identical to those of the incident driving field. Therefore, the nonlinear atomic system scatters light as a linear classical scatterer. Our results are consistent with the recent theory of coherently radiating spin states. The presented Heisenberg-Langevin approach should be simple to generalize for treating superradiance beyond the permutation-symmetric Dicke model.

For the relativistic tunneling effect described using Dirac's equation, Winful et al. [Phys. Rev. A 70, 052112 (2004)] presented the deduction of a general result that allows for the determination of the phase time (group delay) as the sum of the particle dwell time inside a potential barrier and of the self-interference delay associated with the incident and reflected wave functions interaction. In this paper, a mathematical model is derived through a construction analogous to the proposal mentioned above, but based on an alternative representation for Dirac's equation. This representation is similar to the one introduced by Ajaib [Found. Phys. 45, 1586 (2015)]. Thus, from the application of this model in the study of the tunneling effect in the absence of an external magnetic field, the influence of spin on the tunneling times is described. More specifically, the tunneling time is obtained as the sum of the dwell times inside the potential barrier for particles with spin up and spin down and the self-interaction time associated with the incident and reflected wave functions for particles with spin up.

Fidelity estimation is essential for the quality control of entanglement distribution networks. Because measurements collapse quantum states, we consider a setup in which nodes randomly sample a subset of the entangled qubit pairs to measure and then estimate the average fidelity of the unsampled pairs conditioned on the measurement outcome. The proposed estimation protocol achieves the lowest mean-square estimation error in a difficult scenario with arbitrary noise and no prior information. Moreover, this protocol is implementation friendly because it only performs local Pauli operators according to a predefined sequence. Numerical studies show that compared to existing fidelity estimation protocols, the proposed protocol reduces the estimation error in both scenarios with independent and identically distributed noise and correlated noise.