We investigate signatures of chaos and equilibration in the quantum Rabi model, which exhibits a quantum phase transition when the ratio of the atomic level-splitting to bosonic frequency grows to infinity. We show that the out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase and undergoes exponential growth in the superradiant phase, which is associated with the onset of quantum chaos. Furthermore, we show that the effective time-averaged dimension of the quantum Rabi system can be large compared with the spin system size, which leads to suppression of the temporal fluctuations and equilibration of the spin system.

Hyperentanglement of photonic light modes is a valuable resource in quantum information processing and quantum communication. Here we propose a protocol using the interference of two optical nonlinearities and control of the heralding (detection) basis in the orbital angular momentum degree of freedom. This setup is capable of generating states which are both maximally entangled and hyperentangled in at least four dimensions. The resultant state in the four-dimensional case is a generalization of the so-called NOON state (a maximally path-entangled state well known in quantum optics). The production of this state is “perfect” (in other words noiseless) at least in the ideal case, excluding experimental imperfections. The presented setup is very versatile, and with control of the detection and pumping protocols a massively large parameter space, of arbitrarily large dimensionality, may be searched for other states of interest. Also, we present a few specific cases to demonstrate the versatility of the system.

We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multicopy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is suboptimal in this multicopy case. Furthermore, for a large class of multicopy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least 2 in error-probability exponent compared to the multicopy quantum Chernoff bound. This behavior has a classical analog in the performance gap between soft-decision and hard-decision receivers for detecting a multicopy signal embedded in white Gaussian noise.

The search of an unstructured database amounts to finding one element having a certain property out of $N$ elements. The classical search with an oracle checking one element at a time requires on average $N/2$ steps. The Grover algorithm for the quantum search and its unitary Hamiltonian evolution analog accomplish the search asymptotically optimally in $O\left(\sqrt{N}\right)$ time steps. We reformulate the search problem as a dissipative, incoherent Markov process acting on an $N$-level system weakly coupled to a thermal bath. Assuming that the energy levels of the system represent the database elements, we show that, with a proper choice of the spectrum and long-range but bounded transition rates between the energy levels, the system relaxes to the ground state, corresponding to the sought element, in time $O(lnN)$.

In a typical scenario of quantum remote sensing, a server at the remote site sends the sensing information to the local site, so that the client there can make a diagnosis about the sensed field. In practice, the reliability of the sensing information may be undermined by kinds of errors, e.g., the imperfections of measurement devices or the attacks from a malicious eavesdropper. An alternative way to circumvent this problem is to encode the sensing information into entangled states, of which the form can be inferred in a device-independent manner, namely, self-testing. In this paper, we propose a protocol to make secure sensing of a parameter at the remote side. Upon receiving the remote sensing data, the local client can figure out the parameter range by inspecting the joint probabilities. In stark contrast, a malicious eavesdropper who is allowed to access all the remote data cannot either acquire the information of the parameter or cheat the client by replacing returned data with fake ones. We apply this protocol to a magnetic sensing scenario, and we show that the client can reliably estimate the strength range of the magnetic field, which could be intimately related to various mineral resources. Consequently, the client should not overslip any mineral resources by identifying the upper bound of magnetic strength. We also show that our protocol is valid even if the entangled states are mildly noisy.

In quantum weak measurement, a weak value is a quantity related to a pointer shift of a measuring device which is usually determined by pre- and postselection states. For conventional weak measurement, a single weak-value model has been well addressed in precision metrology of time delay, but it only holds for a narrowband light source. To further improve the measurement accuracy, a broad-spectrum light source is needed. We find that the single weak-value model no longer holds, due to the occurrence of modified preselection states. Here, a multiple weak-value model is established by introducing the modified preselection states in the estimation of time delay. For broad-spectrum light source with 50-nm spectral width, the multiple weak-value scheme enables us to achieve a high resolution of $1.6\times {10}^{-4}\mathrm{as}$. Our proposed multiple weak-value amplification may have important applications in various fields involving precise time-delay detection.

Recent improvements in the resonant-state expansion (RSE), focusing on the static mode contribution, have made it possible to treat transverse-magnetic (TM) modes of a spherically symmetric system with the same efficiency as their transverse-electric (TE) counterparts. We demonstrate here that the efficient inclusion of static modes in the RSE results in its quick convergence to the exact solution regardless of the static mode set used. We then apply the RSE to spherically symmetric systems with continuous radial variations of the permittivity. We show that in TM polarization, the spectral transition from whispering gallery to Fabry-Pérot modes is characterized by a peak in the mode losses and an additional mode as compared to TE polarization. Both features are explained quantitatively by the Brewster angle of the surface reflection which occurs in this frequency range. Eliminating the discontinuity at the sphere surface by using linear or quadratic profiles of the permittivity modifies this peak and increases the Fabry-Pérot mode losses, in qualitative agreement with a reduced surface reflectivity. These profiles also provide a nearly parabolic confinement for the whispering gallery modes, for which an analytical approximation using the Morse potential is presented. Both profiles result in a reduced TE-TM splitting, which is shown to be further suppressed by choosing a profile radially extending the mode fields. Based on the concepts of ray optics, phase analysis of the secular equation, and effective quantum-mechanical potential for a wave equation, we discuss a number of useful approximations which shed light on the physical phenomena observed in the spectra of graded-index systems.

We study the resonant modes in double-layered transformation cavities consisting of inner and outer layer boundaries where the mode intensity is mainly located inside the inner layer. This is an intermediate design between a transformation cavity and a cavity in a wholly transformed space of transformation optics. We demonstrate the crossover between these two extreme cases as the outer layer of the cavity varies and also explore the properties of the resonant modes in the cavity. While the near-field patterns of the resonant modes do not change as the outer layer becomes larger, the $Q$ factors approach those of a cavity in the wholly transformed space of transformation optics, and the far-field patterns are modified.

Quantum-key-distribution (QKD) protocols allow exchanging a cryptographic key between two parties. With the development of the Internet, however, all forms of communications consume a huge number of cryptographic keys. Improving the secure key rate of QKD is becoming increasingly important. Quantum compression and key expansion are two ways to increase the secure key rate. In this paper, we propose a quantum-key-expansion (QKE) protocol. A series of singlet states are compressed by number-state-entanglement-preserving tensors and disentanglers to obtain a compressed two-body-entangled state. The cryptographic key is expanded by the number-state-entanglement-preserving tensor network. The advantages of the proposed QKE protocol over the classical-key-expansion algorithm in the key-expansion method, the key length, and the security are discussed in this study. Moreover, due to the structure of the number-state-preserving compression tensor network, our protocol can resist the intercept-resend attack, entanglement-and-measurement attack, and coherent attack.

The landmark Grover algorithm for amplitude amplification serves as an essential subroutine in various types of quantum algorithms, with guaranteed quantum speedup in query complexity. However, there has been no proposal to realize the original motivating application of the algorithm, i.e., the database search or more broadly the pattern matching in a practical setting, mainly due to the technical difficulty in efficiently implementing the data loading and amplitude amplification processes. In this paper, we propose a quantum algorithm that approximately executes the entire Grover database search or pattern matching algorithm. The key idea is to use the recently proposed approximate amplitude encoding method on a shallow quantum circuit, together with the easily implementable inversion-test operation for realizing the projected quantum state having similarity to the query data, followed by the amplitude amplification operation that is independent to the target data index. We provide a thorough demonstration of the algorithm in the problem of image pattern matching.

By introducing four-phase modulations into round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol, the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol is proposed. According to the security proof of RRDQPS protocol, it is able to tolerate a higher error rate of key bits. However, its performance with a practical weak coherent source is still unknown since that security proof only applies to a single photon source. In this article, we give the security proof for the general $n$-photon RRDQPS protocol, by which RRDQPS with a practical weak coherent source becomes feasible in the experiment. Through numerical simulation, it is verified that RRDQPS protocol has an advantage over RRDPS protocol on transmission distance, especially when the pulse number is small.

Leggett-Garg's inequalities predict sharp bounds for some classical correlation functions that address the quantum or classical nature of real-time evolutions. We experimentally observe the violations of these bounds on single- and multiqubit systems, in different settings, exploiting the IBM Quantum platform. In the multiqubit case, we introduce the Leggett-Garg-Bell's inequalities as an alternative to the previous ones. Measuring these correlation functions, we find quantum error mitigation to be essential to spot inequalities violations. Accessing only two qubit readouts, we assess Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum coherence witnesses to be used for investigating quantum hardware, among those introduced. Our analysis highlights the limits of current quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.

In this theoretical manuscript I propose a scheme for entangling a single-electron-semiconductor spin qubit with a single-electron-semiconductor charge qubit in a triangular triple-quantum-dot configuration. Two out of three quantum dots are used to define a single-electron-semiconductor charge qubit. Furthermore, the spin qubit is embedded in the Zeeman sublevels of the third quantum dot. Combining single-qubit gates with entangling controlled-not gates allows one to construct a swap gate and therefore to use the semiconductor spin qubit as a long-lived memory for the semiconductor charge qubit.

In this paper we examine disorder (i.e., static imperfections in manufacture) for the fixed-Hamiltonian evolution protocol of quantum state transfer. We improve the performance by optimizing the choice of Hamiltonian and by implementing an encoding and decoding procedure on small regions at either end of the chain. We find that encoding in only the single-excitation subspace is optimal and provides substantial enhancement to the operating regime of these systems.

We present an encoding technique that reduces the effects of noise on quantum spin systems whose operation is driven by Hamiltonian evolution. This technique is widely applicable, being most relevant to the scenarios where there are insufficient qubits to permit full-scale error correction. Instead, our technique can be implemented over small numbers of qubits and still leads to noticeable improvements in the fidelity of operations. The encoding scheme is easy to implement, flexible with respect to choice of Hamiltonian, and close to optimal.

We investigate the feasibility of observing matter-wave interference of a micron-sized charged particle by putting it into a quantum superposition of states with a distinguishable separation. In the proposed method, an atomic ion is confined in a linear Paul trap along with the massive charged particle so that we can make use of the extensive toolbox of experimental techniques developed to control quantum states of trapped ions and to manipulate their motions with high-fidelity operations. This approach provides a stringent test of the predictions of dynamical reduction models of delocalized quantum superpositions of a particle, reaching macroscopicities of up to $\mathcal{M}=17$. This compares favorably with other proposed approaches and incentivizes the refinement of experimental techniques.

We develop finite-temperature strong-coupling expansions for the $\mathrm{SU}\left(N\right)$ Hubbard model in powers of $\beta t, w=exp(-\beta U)$ and $\frac{1}{\beta U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order of the bandwidth, the expansions converge over a wide temperature range $t^2/U\lesssim T\lesssim 10U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high-temperature expansion for a dressed $\mathrm{SU}\left(N\right)$ Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges, and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\to 0$ limit corresponds to an effective $t\text{−}J$ model. The onset of strong correlations can be identified by a plateaulike behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\delta =1-n$, the deviation from one particle per site, where the leading $\beta t$-dependent terms correspond to holes sloshing around in a disordered $\mathrm{SU}\left(N\right)$ background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

We report on the experimental demonstration of a horizontal accelerometer based on atom interferometry using counterpropagative Raman transitions between the states $|F=1,m_F=\mp 1\rangle$ and $|F=2,m_F=\pm 1\rangle$ of ${}^{87}\mathrm{Rb}$. Compared to the $|F=1,m_F=0\rangle \leftrightarrow |F=2,m_F=0\rangle$ transition usually used in atom interferometry, our scheme presents the advantages of having only a single counterpropagating transition allowed in a retroreflected geometry, using the same polarization configuration as the magneto-optical trap, and allowing the control of the atom trajectory with magnetic forces. We demonstrate horizontal acceleration measurement in a close-to-zero velocity regime using a single-diffraction Raman process with a short-term sensitivity of $25\times {10}^{-5}$ m ${\mathrm{s}}^{-2} {\mathrm{Hz}}^{-1/2}$ and resolution down to $3.8\times {10}^{-6}$ m ${\mathrm{s}}^{-2}$ at an integration time of 3300 s. We discuss specific features of the technique such as spontaneous emission, light shifts, and effects of magnetic field inhomogeneities. We finally give possible applications of this technique in metrology or for cold-atom inertial sensors dedicated to onboard applications.

While quantum fluctuations in binary mixtures of bosonic atoms with short-range interactions can lead to the formation of a self-bound droplet, for equal intracomponent interactions but an unequal number of atoms in the two components, there is an excess part that cannot bind to the droplet. Imposing confinement, as here through periodic boundary conditions in a one-dimensional setting, the droplet becomes amalgamated with a residual condensate. The rotational properties of this compound system reveal simultaneous rigid-body and superfluid behavior in the ground state and uncover that the residual condensate can carry angular momentum even in the absence of vorticity. In contradiction to the intuitive idea that the superfluid fraction of the system would be entirely made up of the excess atoms not bound by the droplet, we find evidence that this fraction is higher than what one would expect in such a picture. Our findings are corroborated by an analysis of the elementary excitations in the system, and shed new light on the coexistence of localization and superfluidity.