Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the nonrelativistic regime. Only unitary transformations are considered with detection processes described by generalized measurements (positive operator valued measures). One-time conditional probabilities are unambiguously derived via the Gleason-Bush theorem, including for puzzling cases like the Wigner's-friend scenario where their form underlines the relativity aspect of measurements. No paradoxical situations emerge, and the roles of Wigner and Wigner can be seen by his friend as being in a superposition.

Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we present the necessary and sufficient conditions under which a mixed state can be distilled into a pure coherent state via stochastic incoherent operations (sIOs). With the help of this result, we further show the following: (i) Any two-dimensional coherent state is distillable via sIOs if and only if it is a pure coherent state; (ii) a state $\rho$ is $n$-distillable via sIOs if and only if it is 1-distillable; and (iii) the set of distillable states via stochastic maximally incoherent operations is identical to the set of distillable states via sIOs. Finally, we analyze the reason why sIO is stronger than stochastic strictly incoherent operations when we use them to distill a coherent state.

We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity—which can be measured by a single measurement setting—followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) $N$-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the $N$-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.

I propose an efficient method for measuring nonlinear coupling between the collective axial breathing mode and the radial rocking mode induced by the mutual Coulomb repulsion in linear ion crystal. The quantum sensing technique is based on the laser-induced coupling between one of the vibrational modes and the internal ion's spin states which allows to estimate the nonlinear coupling either by measuring the phonon probability distribution or by directly observing the Ramsey-type oscillations of the ion spin states. I show that due to the presence of nonlinear phonon coupling the off-resonance interaction between the ion spin states and the axial breathing mode leads to spin-dependent phonon squeezing of the radial rocking mode. Thus the nonlinear coupling can be estimated by measuring population distribution of the motional squeezed state. Furthermore, I show that the off-resonance interaction between the spin and the radial rocking mode creates a spin-dependent beam splitter operation between the two vibrational modes. Thus the parameter estimation can be carried out by detecting the ion spin populations. Finally, I show that the measurement uncertainty precision can reach the Heisenberg limit by using an entangled state between the two collective modes.

The scalar and tensor components of the electric quadrupole (E2) polarizabilities of the first two excited states of all the alkali-metal atoms are determined. To validate the calculations, we have evaluated the ground state E2 polarizabilities of these atoms and compared them with the literature values. We could not find the ground state E2 polarizability value for Fr in the literature to compare with our result. The dominant parts of these quantities are estimated by combining the precisely calculated E2 transition matrix elements of many low-lying transitions with the experimental energies, while the other contributions are estimated using lower-order methods. Our estimated values for the ground states of the above atoms are in good agreement with the literature values suggesting that our estimated E2 polarizabilities for the excited states of the alkali atoms, which were not known earlier except for the Li atom, are also quite accurate. These reported E2 polarizabilities could be useful in guiding many precision measurements in the alkali atoms.

We demonstrate experimentally the generation of one-dimensional cold gases of ${}^{87}\mathrm{Rb}$ atoms by diffuse laser cooling. A horizontal slender vacuum glass tube with a length of 105 cm and diameter of 2 cm is used in our experiment. The diffuse laser light inside the tube, which is generated by multireflection of injected lasers, cools the background vapor atoms. With 250 mW of cooling light and 50 mW of repumping light, an evenly distributed 1-m-long profile of cold atom cloud is obtained. We observe a factor 4 improvement in the atomic optical density for a typical cooling duration of 170 ms and a sub-Doppler atomic temperature of 25 $\mu \mathrm{K}$. The central number of detected cold atoms remains constant for a free-fall duration of 30 ms. Such samples are ideal for many quantum optical experiments involving electromagnetically induced transparency, electronically highly excited (Rydberg) atoms, and quantum precision measurements.

We theoretically investigate superfluid properties of a one-dimensional annular superfluid with a boost. We derive the formula of the superfluid fraction in the one-dimensional superfluid, which was originally derived by Leggett in the context of supersolid. We see that the superfluid fraction given by Leggett's formula detects the emergence of solitons in the one-dimensional annular superfluid. The formation of a bright soliton at a critical interaction strength decreases the superfluid fraction. At a critical boost velocity, a node appears in the soliton and the superfluid fraction vanishes. With a transverse dimension, the soliton alters to a more localized one and it undergoes dynamical instability at a critical transverse length. Consequently, the superfluid fraction decreases as one increases the length up to the critical length. With a potential barrier along the ring, the uniform density alters to an inhomogeneous configuration and it develops a soliton localized at one of the potential minima by increasing the interaction strength.

We address the existence and stability of multipole quantum droplets in symmetric binary Bose-Einstein condensates described by the amended Gross-Pitaevskii equation with Lee-Huang-Yang quantum corrections. Quantum droplets trapped in a weakly anharmonic potential can be composed of different numbers of globally linked poles with an azimuthally periodic distribution. Due to the competing Lee-Huang-Yang-augmented nonlinearity, the norm of two branches of droplets with slopes of opposite sign merges together at a lower cutoff of chemical potential. The lower and upper branches of droplets at the same chemical potential, but with a different norm, can evolve stably in certain parameter regions simultaneously. The stability domain of droplets shrinks with the growth of the number of poles. Even unstable necklacelike droplets can survive for a very long time.

Using a general Hamiltonian treatment, we theoretically study the generation of degenerate quadrature squeezing in a dual-pumped integrated microring resonator coupled to a waveguide. Considering a dual-pump four-wave mixing configuration in an integrated ${\text{Si}}_3{\text{N}}_4$ platform, and following the coupled-mode theory approach, we investigate the effects of parasitic quantum nonlinear optical processes on the generation of squeezed light. Considering five resonance modes in this approach allows us to include the most important four-wave mixing processes involved in such a configuration. We theoretically explore the effects of the pump detunings on different nonlinear processes and show that the effects of some of the parasitic processes are effectively neutralized by symmetrically detuning the two pumps. This yields a significant enhancement in the output squeezing quality without physically changing the structure, but suffers from the trade-off of requiring substantially higher pump power for a fixed target level of squeezing.

We propose a geometric phase plate (GPP) assisted optical resonator to tailor and discriminate intracavity transverse modes. Theoretical analysis demonstrates that the resonator has well-defined self-consistent resonator modes when the GPP is placed at the self-imaging position of the resonator mirror. By engineering phases carried by the GPP, we show configuration functions including breaking the symmetry of transverse-mode structures in forward and backward propagations, generating purely high-order transverse modes, and discriminating degenerate Laguerre-Gaussian modes. Furthermore, we conduct numerical simulation based on the iterative Fox-Li method. Our design provides a tool for efficiently shaping laser modes at a source, which has potential application in such technologies as optical imaging, optical tweezers, optical communication, and quantum information processing.

A logarithmic Schrödinger equation with time-dependent coupling to the nonlinearity is presented as a model of collisional decoherence of the wave function of a quantum particle in position space. The particular mathematical form of the logarithmic Schrödinger equation has been shown to follow from conditional wave theory, but the validity of the logarithmic Schrödinger equation has not yet been investigated numerically for general initial conditions. Using an operator-splitting approach, we solve the nonlinear equation of motion for the wave function numerically and compare it to the solution of the standard Joos-Zeh master equation for the density matrix. We find good agreement for the time-dependent behavior of the ensemble widths between the two approaches, but note curious zero-pinning behavior of the logarithmic Schrödinger equation, whereby the zeros of the wave function are not erased by continued propagation. By examining the derivation of the logarithmic Schrödinger equation from conditional wave theory, we indicate possible avenues of resolution to this zero-pinning problem.

Nonlocality and quantum measurement are two fundamental topics in quantum theory and their interplay attracts intensive focuses since the discovery of Bell theorem. Recently, nonlocality sharing among multiple observers with one entangled pair has been predicted and experimentally observed by generalized quantum measurement—weak measurement. However, only the one-sided sequential case, i.e., one Alice and multiple Bobs, is widely discussed and little is known about the two-sided case. Here, we theoretically and experimentally explore the nonlocality sharing in the two-sided sequential measurements case in which one entangled pair is distributed to multiple Alices and Bobs. We experimentally observed double Einstein-Podolsky-Rosen (EPR) steering among four observers in a photonic system. In the case that all observers adopt the same measurement strength of the weak measurement, it is observed that double EPR steering can be demonstrated simultaneously. The results not only deepen our understanding of relation between sequential measurements and nonlocality but also may find important applications in many quantum information tasks, such as randomness certification.

The study of entanglement properties of multiqubit states that are invariant under permutations of qubits is motivated by potential applications in quantum computing, quantum communication, and quantum metrology. In this work we generalize the notions of symmetrization, Dicke states, and the Majorana representation to the alternating, cyclic, and dihedral subgroups of the full group of permutations. We use these tools to characterize states that are invariant under these subgroups and analyze their entanglement properties.

Quantum transport in a one-dimensional (1D) quasiperiodic lattice with mobility edges is explored. We first investigate the adiabatic pumping between left and right edge modes by resorting to two edge-bulk-edge channels and demonstrate that the success or failure of the adiabatic pumping depends on whether the corresponding bulk subchannel undergoes a localization-delocalization transition. Compared with the paradigmatic Aubry-André model, the introduction of mobility edges triggers an opposite outcome for successful pumping in the two channels, showing a discrepancy of the critical condition, and facilitates the robustness of the adiabatic pumping against quasidisorder. We also consider the transfer between excitations at both boundaries of the lattice, and an anomalous phenomenon characterized by the enhanced quasidisorder contributing to the excitation transfer is found. Furthermore, there exists a parametric regime where a nonreciprocal effect emerges in the presence of mobility edges, which leads to a unidirectional transport for the excitation transfer and enables potential applications in the engineering of quantum diodes.

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.