Author(s): Chunfeng Wu, Yimin Wang, Chu Guo, Yingkai Ouyang, Gangcheng Wang, and Xun-Li Feng

Recently, there has been growing interest in using quantum error correction in practical devices. A central issue in quantum error correction is the initialization of quantum data into a quantum error-correction code. Most studies have concentrated on generating quantum codes based on their encoding...

[Phys. Rev. A 99, 012335] Published Tue Jan 22, 2019

Author(s): Lin Chen, Yu Yang, and Wai-Shing Tang

We present the positive-partial-transpose (PPT) square conjecture introduced by M. Christandl *Banff International Research Station Workshop: Operator Structures in Quantum Information Theory* (Banff International Research Station, Alberta, 2012). We prove the conjecture in the case n=3 as a consequen...

[Phys. Rev. A 99, 012337] Published Tue Jan 22, 2019

Author(s): Matthew Otten and Stephen K. Gray

We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems, but we illustrate it with applications to quantum information and quantum sensing. The ...

[Phys. Rev. A 99, 012338] Published Tue Jan 22, 2019

Author(s): Xiao-Bin Liang, Bo Li, and Shao-Ming Fei

In a recent paper, M. F. Sacchi [Phys. Rev. A **96**, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show that the analytical solutions in some cases are invalid. In thi...

[Phys. Rev. A 99, 016301] Published Tue Jan 22, 2019

Author(s): D. Martínez, M. A. Solís-Prosser, G. Cañas, O. Jiménez, A. Delgado, and G. Lima

High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of D-dimensional quantum systems. Such progress has fueled the search of reliable quantum tomographic methods aiming for the characterization of thes...

[Phys. Rev. A 99, 012336] Published Tue Jan 22, 2019

Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the interactions between the active components are represented via an effective density-dependent diffusivity in a mean-field single-particle description. Here, a new class of scalar active matter is proposed by incorporating a diffusivity edge into the dynamics: when the local density of the system surpasses a critical threshold, the diffusivity vanishes. The effect of the diffusivity edge is studied under the influence of an external potential, which introduces the ability to control the behaviour of the system by changing an effective temperature, which is defined in terms of the single-particle diffusivity and mobility. At a critical effective temperature, a system that is trapped by a harmonic potential is found to undergo a condensation transition, which manifests formal similarities to Bose-Einstein condensation.

We show that there are six inequivalent $4\times4$ unextendible product bases (UPBs) of size eight, when we consider only 4-qubit product vectors. We apply our results to construct Positive-Partial-Transpose entangled states of rank nine. They are at the same 4-qubit, $2\times2\times4$ and $4\times4$ states, and their ranges have product vectors. One of the six UPBs turns out to be orthogonal to an almost genuinely entangled space, in the sense that the latter does not contain $4\times4$ product vector in any bipartition of 4-qubit systems. We also show that the multipartite UPB orthogonal to a genuinely entangled space exists if and only if the $n\times n\times n$ UPB orthogonal to a genuinely entangled space exists for some $n$. These results help understand an open problem in [Phys. Rev. A 98, 012313, 2018].

Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or more channels through partial trace out of a broadcasting channel. We see that covariance conditions can be used to simplify compatibility conditions as the broadcasting channel can be assumed to be covariant in a particular way. A particular emphasis is on Weyl covariance and in determining compatibility conditions for Weyl-covariant channels. The concrete examples studied include the case of a non-compact continuous phase space and the case of a finite phase space.

We describe a general procedure to give effective continuous descriptions of quantum lattice systems in terms of quantum fields. There are two key novelties of our method: firstly, it is framed in the hamiltonian setting and applies equally to distinguishable quantum spins, bosons, and fermions and, secondly, it works for arbitrary variational tensor network states and can easily produce computable non-gaussian quantum field states. Our construction extends the mean-field fluctuation formalism of Hepp and Lieb (developed later by Verbeure and coworkers) to identify emergent continuous large-scale degrees of freedom - the continuous degrees of freedom are not identified beforehand. We apply the construction to to tensor network states, including, matrix product states and projected entangled-pair states, where we recover their recently introduced continuous counterparts, and also for tree tensor networks and the multi-scale entanglement renormalisation ansatz. Finally, extending the continuum limit to include dynamics we obtain a strict light cone for the propagation of information.

Accurate, nontrivial quantum operations on many qubits are experimentally challenging. As opposed to the standard approach of compiling larger unitaries into sequences of 2-qubit gates, we propose a protocol on Hamiltonian control fields which implements highly selective multi-qubit gates in a strongly-coupled many-body quantum system. We exploit the selectiveness of resonant driving to exchange only 2 out of $2^N$ eigenstates of some background Hamiltonian, and discuss a basis transformation, the eigengate, that makes this operation relevant to the computational basis. The latter has a second use as a Hahn echo which undoes the dynamical phases due to the background Hamiltonian. We find that the error of such protocols scales favourably with the gate time as $t^{-2}$, but the protocol becomes inefficient with a growing number of qubits N. The framework is numerically tested in the context of a spin chain model first described by Polychronakos, for which we show that an earlier solution method naturally gives rise to an eigengate. Our techniques could be of independent interest for the theory of driven many-body systems.

In order to explore the effect of external temperature $T$ in quantum correlation we compute thermal entanglement and thermal discord analytically in the Heisenberg $X$ $Y$ $Z$ model with Dzyaloshinskii-Moriya Interaction term ${\bm D} \cdot \left( {\bm \sigma}_1 \times {\bm \sigma}_2 \right)$. For the case of thermal entanglement it is shown that quantum phase transition occurs at $T = T_c$ due to sudden death phenomenon. For antiferromagnetic case the critical temperature $T_c$ increases with increasing ${\bm D}$. For ferromagnetic case, however, $T_c$ exhibits different behavior in the regions $|{\bm D}| \geq |{\bm D_*}|$ and $|{\bm D}| < |{\bm D_*}|$, where ${\bm D_*}$ is particular value of ${\bm D}$. It is shown that $T_c$ becomes zero at $|{\bm D}| = |{\bm D_*}|$. We explore the behavior of thermal discord in detail at $T \approx T_c$. For antiferromagnetic case the external temperature makes the thermal discord exhibit exponential damping behavior, but it never reaches at exact zero. For ferromagnetic case the thermal entanglement and thermal discord are shown to be zero simultaneously at $T_c = 0$ and $|{\bm D}| = |{\bm D_*}|$. This is unique condition for simultaneous disappearance of thermal entanglement and thermal discord in this model.

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin-orbit coupled Bose-Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play important role in the experiments of BEC with artificial gauge fields.

The evolution of quantum light through linear optical devices can be described by the scattering matrix $S$ of the system. For linear optical systems with $m$ possible modes, the evolution of $n$ input photons is given by a unitary matrix $U=\varphi_{m,M}(S)$ given by a known homomorphism, $\varphi_{m,M}$, which depends on the size of the resulting Hilbert space of the possible photon states, $M$. We present a method to decide whether a given unitary evolution $U$ for $n$ photons in $m$ modes can be achieved with linear optics or not and the inverse transformation $\varphi_{m,M}^{-1}$ when the transformation can be implemented. Together with previous results, the method can be used to find a simple optical system which implements any quantum operation within the reach of linear optics. The results come from studying the adjoint map bewtween the Lie algebras corresponding to the Lie groups of the relevant unitary matrices.

Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements thus providing a significant advantage over previously used methods. We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.

Correlation functions unequivocally define the dynamics of classical systems. This represents a fundamental difference with respect to quantum systems, for which an infinite number of mutually incompatible dynamics can be inferred depending upon the measurement scheme. We provide two sufficient conditions for the non-contextuality of correlation functions. The first one defines a general class of experiments where measured correlation functions are unambiguously defined in terms of two-time Heisenberg operators. Correlation functions written in this way cannot be associated to a backaction-evading measurement, and, thus, are not representative of the unperturbed dynamics of a quantum system. Contrarily, our second condition, which is established for systems consisting of a large number of particles, yields a backaction-free correlation function in the weak-interaction limit. This last condition can be reinterpreted in terms of collective measurements and shows that cheating quantum backaction using collective operations comes at the price of washing-out quantum uncertainty.

Coupled parametric oscillators have been recently employed as simulators of artificial Ising networks, with the potential to efficiently solve computationally hard minimization problems. We report on a detailed study of two coupled degenerate parametric oscillators, exploring the entire phase diagram, in terms of pump power, phase and coupling strength, both analytically and experimentally in a radio-frequency (RF) experiment. In addition to a regime where the oscillators act as coupled spin-1/2 degrees of freedom, we predict and observe a wide range of parameters in the vicinity of the oscillation threshold where the spin-1/2 description does not apply. In this regime, the oscillators never synchronize, but rather show persistent, full-scale, coherent beats, whose frequency reflects the coupling strength. Our comprehensive study can be used as the the building block of a coherent Ising machines that combine dissipative and conservative couplings.

We employ numerically exact methods to study a qubit coupled to a quantum-mechanical bath, focusing on important correlation effects such as the Lamb shift and entanglement that are typically neglected in the modeling of contemporary quantum computers. We find a fundamental trade-off between speed and accuracy in qubit initialization which is important in the optimization of future reset protocols. Namely, we show analytically that at low temperatures, the deviation from the bare qubit ground state is proportional to the qubit decay rate, caused by the unavoidable entanglement between the qubit and the bath. We also find that the qubit decay is superexponential at short time scales, contrary to the result from standard Markovian approaches. However, the fidelities of quantum logic gates can be sufficiently accurately predicted by the Markovian methods. Our results can be used to develop quantum devices with engineered environments and to guide future experiments in probing the properties of the reservoirs.

The precision of a quantum sensor can overcome its classical counterpart when its constituants are entangled. In gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of non-classical states of the electronic spin $J=8$ of dysprosium atoms, created using light-induced non-linear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.

Charge dynamics in an ultra-cold setup involving a laser dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the vibrational motion of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. Aspects of the transport such as its direction can be controlled by the excitation laser. This leads to new directions in the investigation of hybrid atom-ion systems that can be experimentally explored using optically trapped strontium atoms.

Periodically-tapered-waveguides technique is an emerging potential route to establish quasi-phase-matching schemes for efficient on-demand parametric interactions in third-order nonlinear materials. In this paper, I investigate this method in enhancing spontaneous photon-pairs emission in fibres and planar waveguides with sinusoidally-varying cross sections. I have developed a general robust quantum model to study this process under continuous or pulsed-pump excitations. The model shows a great enhancement in photon-pairs generation in waveguides with a small number of tapering periods that are feasible via the current fabrication technologies. I envisage that this work will open a new area of research to investigate how the tapering patterns can be fully optimised to tailor the spectral properties of the output photons in third-order nonlinear guided structures.