We investigate the problem of computing optimal quantum measurements in both minimal measuring and minimax strategies. A Belavkin weighted square-root measurement (BWSRM) with appropriate weights can represent the measurement that maximizes the correct probability for any given prior probabilities of quantum states. Using this fact, we propose methods for computing optimal solutions by optimizing the weights of the BWSRM. First, we explain the conditions for the BWSRM to be optimal. In particular, we argue that if a BWSRM with certain weights is a minimax measurement, then the minimax probabilities can be immediately obtained. Next, we propose an extension of the iterative algorithm developed by Ježek et al. [Phys. Rev. A 65, 060301 (2002)] for maximizing the correct probability. We prove that, for a linearly independent pure state set, Ježek et al.'s algorithm converges to an optimal measurement. We also propose an iterative algorithm for a minimax solution and prove that, for a pure state set, our algorithm monotonically decreases the difference between estimated and true minimax values. Finally the performance of our algorithms is evaluated through numerical experiments.

Applying a magnetic-field gradient to a trapped ion allows long-wavelength radiation to produce a mechanical force on the ion's motion when internal transitions are driven. We demonstrate such a coupling using a single trapped ${}^{171}\mathrm{Yb}^{+}$ ion and use it to produce entanglement between the spin and motional state, an essential step toward using such a field gradient to implement multiqubit operations.

We quantitatively analyze and evaluate the controller's power in $N$-qubit controlled teleportation schemes. We calculate the minimum control power required to ensure the controller's authority such that the teleportation fidelity without the controller's permission is no more than the classical bound. We revisit several typical controlled teleportation schemes from the controller's point of view and evaluate the control power in these schemes. We find that for teleporting arbitrary $N$-qubit states, each controller should control at least $N$ bits of useful information to ensure his or her authority over the protocol. We also discuss the general rules that must be satisfied by controlled teleportation schemes to ensure both teleportation fidelity and control power.

We consider an infinite class of unambiguous quantum state discrimination problems on multipartite systems, described by Hilbert space $\mathcal{H}$, of any number of parties. Restricting consideration to measurements that act only on $\mathcal{H}$, we find the optimal global measurement for each element of this class, achieving the maximum possible success probability of $1/2$ in all cases. This measurement turns out to be both separable and unique, and by our recently discovered necessary condition for local quantum operations and classical communication (LOCC) it is easily shown to be impossible by any finite-round LOCC protocol. We also show that, quite generally, if the input state is restricted to lie in $\mathcal{H}$, then any LOCC measurement on an enlarged Hilbert space is effectively identical to an LOCC measurement on $\mathcal{H}$. Therefore, our necessary condition for LOCC demonstrates directly that a higher success probability is attainable for each of these problems using general separable measurements as compared to that which is possible with any finite-round LOCC protocol.

Accurate frequency measurements of molecular transitions around $2 \mu \mathrm{m}$ are performed by using a direct-frequency-comb spectroscopy approach that combines an ${\mathrm{Er}}^{+}$ frequency-comb oscillator at $1.5 \mu \mathrm{m}$, a Tm-Ho fiber amplifier, and a Fabry-Perot-filter, high-resolution dispersive spectrometer optical multiplex-detection system. This apparatus has unique performances in terms of a wide dynamic range to integrate the intensity per comb mode, which allows one to measure molecular absorption profiles with high precision. Spectroscopic information about transition frequencies and linewidths is very accurately determined. Relative frequency uncertainties of the order of a few parts in ${10}^{-9}$ are achieved for rovibrational transitions of the ${\mathrm{CO}}_2$ molecule around $5100 {\mathrm{cm}}^{-1}$. Moreover, tiny frequency shifts due to molecular collisions and interacting laser power using direct comb spectroscopy are investigated in a systematic way.

We find that, for sufficiently strong mid-IR fields, transitions between different conduction bands play an important role in the generation of high-order harmonics in a dielectric. The transitions make a significant contribution to the harmonic signal, and they can create a single effective band for the motion of an electron wave packet. We show how high harmonic spectra produced during the interaction of ultrashort laser pulses with periodic solids provide a spectroscopic tool for understanding the effective band structure that controls electron dynamics in these media.

We analyze the non-Markovianity degree for random unitary evolution of $d$-level quantum systems. It is shown how the non-Markovianity degree is characterized in terms of local decoherence rates. In particular we derive a sufficient condition for vanishing of the backflow of information and relate this concept to other characteristics of non-Markovianity.

Qubit-qubit interactions can significantly boost quantum coherence times for Bell states. The coherence-time enhancements are, however, not monotonic and there exists a phase where further increasing the interaction is unhelpful. A resonator in a suggested circuit QED-type implementation of the Tavis-Cummings (Dicke) model, is shown to shift this transition point depending on the number of loaded photons. This allows the resonator to amplify the coherence enhancements in certain regimes. The interactions also induce unusual collapse and revival-type behavior for the entanglement dynamics. An exact open quantum system's formalism–(quasi-Hamiltonians for the Dicke model) shows how a Bell state singlet-triplet qubit in a resonator can be protected against $1/f$ noise from randomly fluctuating two-level systems. Simple circuit level details are given for flux qubits.

In a recent experiment, Kwon et al. [Phys. Rev. A 90, 063627 (2014)] generated a disordered state of quantum vortices by translating an oblate Bose-Einstein condensate past a laser-induced obstacle and studied the subsequent decay of vortex number. Using mean-field simulations of the Gross-Pitaevskii equation, we shed light on the various stages of the observed dynamics. We find that the flow of the superfluid past the obstacle leads initially to the formation of a classical-like wake, which later becomes disordered. Following removal of the obstacle, the vortex number decays due to vortices annihilating and drifting to the boundary. Our results are in excellent agreement with the experimental observations. Furthermore, we probe thermal effects through phenomenological dissipation.

We calculate the stability diagram for a trapped normal Fermi or Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry and temperature on the stability using Hartree-Fock theory. We find that exchange appreciably reduces stability and that, for bosons, the double instability feature in oblate trapping geometries predicted previously is still predicted by the Hartree-Fock theory. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate or degenerate Fermi gas.

We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting the fact that charged dopants locally suppress quantum reflection from the Casimir-Polder potential. We present a general quantum scattering theory for reflection off periodically charged surfaces and discuss the requirements for the observation of multiple diffraction peaks.

Extended wavefronts are used for coherent full field imaging of objects based on solving the inverse Fresnel diffraction problem. To this end, the conventional data correction step is given by division of the recorded object image by the intensity pattern of the empty beam. This division of intensities in the detection plane is a rather crude approximation for the separation of the complex valued object and probing fields. Here we present a quantitative error estimate, along with its mathematical proof, and confirm the prediction with numerical simulations. Finally the problem is illustrated with experimental results.

We test current numerical implementations of laser-matter interactions by comparison with exact analytical results. Focusing on photon emission processes, it is found that the numerics accurately reproduce analytical emission spectra in all considered regimes, except for the harmonic structures often singled out as the most significant high-intensity (multiphoton) effects. We find that this discrepancy originates in the use of the locally constant field approximation.

We introduce one kind of partially coherent beam with a nonconventional correlation function named the Hermite-Gaussian correlated Schell-model (HGCSM) beam. It is found that a HGCSM beam exhibits self-splitting properties on propagation in free space, i.e., the initial single beam spot evolves into two or four beam spots in the far field depending on the initial beam orders, which are closely related to the beam width and coherence widths of the HGCSM beam, and a focused HGCSM beam exhibits splitting and combining properties near the focal plane. Furthermore, we report experimental generation of a HGCSM beam and demonstrate splitting and combining properties of a focused HGCSM beam in experiment. The phenomenon of correlation-induced self-splitting will be useful for attacking multiple targets, trapping multiple particles, and guiding atoms.

We demonstrate photodissociation of ${\mathrm{BeH}}^{+}$ ions within a Coulomb crystal of thousands of ${}^9{\mathrm{Be}}^{+}$ ions confined in a Penning trap. Because ${\mathrm{BeH}}^{+}$ ions are created via exothermic reactions between trapped, laser-cooled ${\mathrm{Be}}^{+}\left({}^2{P}_{3/2}\right)$ and background ${\mathrm{H}}_2$ within the vacuum chamber, they represent a major contaminant species responsible for infidelities in large-scale trapped-ion quantum-information experiments. The rotational-state-insensitive dissociation scheme described here makes use of 157-nm photons to produce ${\mathrm{Be}}^{+}$ and H as products, thereby restoring ${\mathrm{Be}}^{+}$ ions without the need for reloading. This technique facilitates longer experiment runtimes at a given background ${\mathrm{H}}_2$ pressure and may be adapted for removal of ${\mathrm{MgH}}^{+}$ and ${\mathrm{AlH}}^{+}$ impurities.

We use microscopic Bogoliubov–de Gennes formalism to explore the ground-state phase diagram of the single-band attractive Hofstadter-Hubbard model on a square lattice. We show that the interplay between the Hofstadter butterfly and superfluidity breaks spatial symmetry, and gives rise to stripe-ordered superfluid and supersolid phases in large parameter spaces. We also discuss the effects of a trapping potential and comment on the viability of observing stripe-ordered phases with cold Fermi gases.

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.

We investigate the entanglement dynamics of two harmonic oscillators with a weak time-dependent coupling. We find strong connections between the dynamical behaviors of the entanglement and the stability of the normal modes. An abrupt transition of the entanglement dynamics from periodic and bounded to monotonically increasing occurs, when one of the normal modes becomes dynamically unstable as the modulation amplitude crosses the critical value. In particular, when the modulation frequency is roughly twice the oscillator frequency, an explicit critical value for the modulation strength is derived to specify the transition. Moreover, it is found that one can significantly change the dynamical behavior of the entanglement by adding an extremely weak time modulation with specific frequency to a constant coupling.

Quantum entanglement between an arbitrary number of remote qubits is examined analytically. We show that there is a nonprobabilistic way to address in one context the management of entanglement of an arbitrary number of mixed-state qubits by engaging quantitative measures of entanglement and a specific external control mechanism. Both all-party entanglement and weak inseparability are considered. We show that for $N\ge 4$, the death of all-party entanglement is permanent after an initial collapse. In contrast, weak inseparability can be deterministically managed for an arbitrarily large number of qubits almost indefinitely. Our result suggests a picture of the path that the system traverses in the Hilbert space.