Proposing a system of two rotatable nanoparticles (NPs) in the presence of electromagnetic vacuum fluctuations, using the framework of canonical quantization, the electromagnetic and matter fields have been quantized. The non-contact frictional torque, affecting the rotation of NPs due to the presence of electromagnetic vacuum fluctuations and also by the matter field fluctuations have been derived. Considering the distance between NPs less than 100 nm in the near-field, we observe the rotations are phase locked. It has been shown that the electromagnetic vacuum fluctuations play the role of noises to break down the synchronization. Also surprisingly, we find the frictional torque between NPs in the near-field is much bigger than the popular contact friction between them where it causes a robust synchronization in the near-field.

We address the statistics of a simultaneous CWLM of two non-commuting variables on a few-state quantum system subject to a conditioned evolution. Both conditioned quantum measurement and that of two non-commuting variables differ drastically for either classical or quantum projective measurement, and we explore the peculiarities brought by the combination of the two.

We put forward a proper formalism for the evaluation of the distributions of measurement outcomes. We compute and discuss the statistics in idealized and experimentally relevant setups. We demonstrate the visibility and manifestations of the interference between initial and final states in the statistics of measurement outcomes for both variables in various regimes.

We analytically predict the peculiarities at the circle ${\cal O}^2_1+{\cal O}^2_2=1$ in the distribution of measurement outcomes in the limit of short measurement times and confirm this by numerical calculation at longer measurement times. We demonstrate analytically anomalously large values of the time-integrated output cumulants in the limit of short measurement times(sudden jump) and zero overlap between initial and final states, and give the detailed distributions. We present the numerical evaluation of the probability distributions for experimentally relevant parameters in several regimes and demonstrate that interference effects in the conditioned measurement can be accurately predicted even if they are small.

The two degenerate ground states of the anisotropic Heisenberg (XY) spin model of a chain of qubits (pseudo-spins) can encode quantum information, but their degree of protection against local perturbations is known to be only partial. We examine the properties of the system in the presence of non-local spin-spin interactions, possibly emerging from the quantum electrodynamics of the device. We find a phase distinct from the XY phase admitting two ground states which are highly protected against all local field perturbations, persisting across a range of parameters. In the context of the XY chain we discuss how the coupling between two ground states can be used to observe signatures of topological edge states in a small controlled chain of superconducting transmon qubits.

The prospect of quantum simulating lattice gauge theories opens exciting possibilities for understanding fundamental forms of matter. Here, we show that trapped ions represent a promising platform in this context when simultaneously exploiting internal pseudo-spins and external phonon vibrations. We illustrate our ideas with two complementary proposals for simulating lattice-regularized quantum electrodynamics (QED) in (1+1) space-time dimensions. The first scheme replaces the gauge fields by local vibrations with a high occupation number. By numerical finite-size scaling, we demonstrate that this model recovers Wilson's lattice gauge theory in a controlled way. Its implementation can be scaled up to tens of ions in an array of micro-traps. The second scheme represents the gauge fields by spins 1/2, and thus simulates a quantum link model. As we show, this allows the fermionic matter to be replaced by bosonic degrees of freedom, permitting small-scale implementations in a linear Paul trap. Both schemes work on energy scales significantly larger than typical decoherence rates in experiments, thus enabling the investigation of phenomena such as string breaking, Coleman's quantum phase transition, and false-vacuum decay. The underlying ideas of the proposed analog simulation schemes may also be adapted to other platforms, such as superconducting qubits.

Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a mechanism to carry out a quantum adiabatic variant of Grover's search algorithm using a single bosonic particle placed in an optical lattice. By studying the scaling of the gap and relevant matrix element in various spatial dimensions, we show that a quantum speedup can already be gained in three dimensions. We argue that the suggested scheme is realizable with present-day experimental capabilities.

Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^{\dag}$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine stability of absolutely separating maps under tensor product and show that $\Phi^{\otimes N}$ is absolutely separating for any $N$ if and only if $\Phi$ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.

We study energy levels of two heteronuclear molecules moving in a spherically symmetric harmonic trap. A role of electric dipole interactions is compared and contrasted with our earlier results (https://arxiv.org/abs/1512.00631) for two magnetic dipolar atoms. We stress importance of a rotational energy with its value which is very high compared to the energy of dipolar interaction. We show that dipolar forces do not play a significant role in the ground state of the system under typical experimental conditions. However, there exist excited states that exhibit anticrossings similar to the ones observed for magnetic dipoles.

We study two dispersive regimes in the dynamics of $N$ two-level atoms interacting with a bosonic mode for long interaction times. Firstly, we analyze the dispersive multiqubit quantum Rabi model for the regime in which the qubit frequencies are equal and smaller than the mode frequency, and for values of the coupling strength similar or larger than the mode frequency, namely, the deep strong coupling regime. Secondly, we address an interaction that is dependent on the photon number, where the coupling strength is comparable to the geometric mean of the qubit and mode frequencies. We show that the associated dynamics is analytically tractable and provide useful frameworks with which to analyze the system behavior. In the deep strong coupling regime, we unveil the structure of unexpected resonances for specific values of the coupling, present for $N\ge2$, and in the photon-number-dependent regime we demonstrate that all the nontrivial dynamical behavior occurs in the atomic degrees of freedom for a given Fock state. We verify these assertions with numerical simulations of the qubit population and photon-statistic dynamics.

We study the probabilistic (conditional) teleportation protocol when the entanglement needed to its implementation is given by thermal entanglement, i.e., when the entangled resource connecting Alice and Bob is an entangled mixed state described by the canonical ensemble density matrix. Specifically, the entangled resource we employ here is given by two interacting spin-1/2 systems (two qubits) in equilibrium with a thermal reservoir at temperature T. The interaction between the qubits is described by a Heisenberg-like Hamiltonian, encompassing the Ising, the XX, the XY, the XXX, and XXZ models, with or without external fields. For all those models we show analytically that the probabilistic protocol is exactly equal to the deterministic one whenever we have no external field. However, when we turn on the field the probabilistic protocol outperforms the deterministic one in several interesting ways. Under certain scenarios, for example, the efficiency (average fidelity) of the probabilistic protocol is greater than the deterministic one and increases with increasing temperature, a counterintuitive behavior. We also show regimes in which the probabilistic protocol operates with relatively high success rates and, at the same time, with efficiency greater than the classical limit 2/3, a threshold that cannot be surpassed by any protocol using only classical resources (no entanglement shared between Alice and Bob). The deterministic protocol's efficiency under the same conditions is below 2/3, highlighting that the probabilistic protocol is the only one yielding a genuine quantum teleportation. We also show that near the quantum critical points for almost all those models the qualitative and quantitative behaviors of the efficiency change considerably, even at finite T.

The state of a continuously monitored qubit evolves stochastically, exhibiting competition between coherent Hamiltonian dynamics and diffusive partial collapse dynamics that follow the measurement record. We couple these distinct types of dynamics together by linearly feeding the collected record for dispersive energy measurements directly back into a coherent Rabi drive amplitude. Such feedback turns the competition cooperative, and effectively stabilizes the qubit state near a target state. We derive the conditions for obtaining such dispersive state stabilization and verify the stabilization conditions numerically. We include common experimental nonidealities, such as energy decay, environmental dephasing, detector efficiency, and feedback delay, and show that the feedback delay has the most significant negative effect on the feedback protocol. Setting the measurement collapse timescale to be long compared to the feedback delay yields the best stabilization.