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Facilitated quantum cellular automata as simple models with nonthermal eigenstates and dynamics. (arXiv:1802.07729v1 [cond-mat.stat-mech])

Fri, 2018-02-23 02:45

We introduce and describe a class of simple facilitated quantum spin models in which the dynamics is due to the repeated application of unitary gates. The gates are applied periodically in time, so their combined action constitutes a Floquet unitary. The dynamics of the models we discuss can be classically simulated, and their eigenstates classically constructed (although they are highly entangled). We consider a variety of models in both one and two dimensions, involving Clifford gates and Toffoli gates. For some of these models, we explicitly construct conserved densities; thus these models are "integrable." The other models do not seem to be integrable; yet, for some system sizes and boundary conditions, their eigenstate entanglement is strongly subthermal. Some of the models have exponentially many eigenstates in which one or more sites are "disentangled" from the rest of the system, as a consequence of reflection symmetry.

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Contextuality bounds the efficiency of classical simulation of quantum processes. (arXiv:1802.07744v1 [quant-ph])

Fri, 2018-02-23 02:45

Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower bound on the amount of classical memory required to simulate any quantum sub-theory, thereby establishing a quantitative connection between contextuality and classical simulability. We apply our result to the qubit stabilizer sub-theory, where the presence of state-independent contextuality has been an obstacle in establishing contextuality as a quantum computational resource. We find that the presence of contextuality in this sub-theory demands that the minimum number of classical bits of memory required to simulate a multi-qubit system must scale quadratically in the number of qubits; notably, this is the same scaling as the Gottesman-Knill algorithm. We contrast this result with the (non-contextual) qudit case, where linear scaling is possible.

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Communication Complexity of One-Shot Remote State Preparation. (arXiv:1802.07795v1 [quant-ph])

Fri, 2018-02-23 02:45

Quantum teleportation uses prior shared entanglement and classical communication to send an unknown quantum state from one party to another. Remote state preparation (RSP) is a similar distributed task in which the sender knows the entire classical description of the state to be sent. (This may also be viewed as the task of non-oblivious compression of a single sample from an ensemble of quantum states.) We study the communication complexity of approximate remote state preparation, in which the goal is to prepare an approximation of the desired quantum state. Jain [Quant. Inf. & Comp., 2006] showed that the worst-case communication complexity of approximate RSP can be bounded from above in terms of the maximum possible information in an encoding. He also showed that this quantity is a lower bound for communication complexity of (exact) remote state preparation. In this work, we tightly characterize the worst-case and average-case communication complexity of remote state preparation in terms of non-asymptotic information-theoretic quantities. We also show that the average-case communication complexity of RSP can be much smaller than the worst-case one. In the process, we show that n bits cannot be communicated with less than n transmitted bits in LOCC protocols. This strengthens a result due to Nayak and Salzman [J. ACM, 2006] and may be of independent interest.

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A conditionally integrable Schr\"odinger potential of a bi-confluent Heun class. (arXiv:1802.07821v1 [quant-ph])

Fri, 2018-02-23 02:45

We present a bi-confluent Heun potential for the Schr\"odinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This is an infinite potential well defined on the positive half-axis. Each of the fundamental solutions for this conditionally integrable potential is written as an irreducible linear combination of two Hermite functions of a shifted and scaled argument. We present the general solution of the problem, derive the exact energy spectrum equation and construct a highly accurate approximation for the bound-state energy levels.

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Quantum Divide-and-Conquer Anchoring for Separable Non-negative Matrix Factorization. (arXiv:1802.07828v1 [quant-ph])

Fri, 2018-02-23 02:45

It is NP-complete to find non-negative factors $W$ and $H$ with fixed rank $r$ from a non-negative matrix $X$ by minimizing $\|X-WH^\top\|_F^2$. Although the separability assumption (all data points are in the conical hull of the extreme rows) enables polynomial-time algorithms, the computational cost is not affordable for big data. This paper investigates how the power of quantum computation can be capitalized to solve the non-negative matrix factorization with the separability assumption (SNMF) by devising a quantum algorithm based on the divide-and-conquer anchoring (DCA) scheme. The design of quantum DCA (QDCA) is challenging. In the divide step, the random projections in DCA is completed by a quantum algorithm for linear operations, which achieves the exponential speedup. We then devise a heuristic post-selection procedure which extracts the information of anchors stored in the quantum states efficiently. Under a plausible assumption, QDCA performs efficiently, achieves the quantum speedup, and is beneficial for high dimensional problems.

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Tutorial: Magnetic resonance with nitrogen-vacancy centers in diamond---microwave engineering, materials science, and magnetometry. (arXiv:1802.07857v1 [cond-mat.mtrl-sci])

Fri, 2018-02-23 02:45

This tutorial article provides a concise and pedagogical overview on negatively-charged nitrogen-vacancy (NV) centers in diamond. The research on the NV centers has attracted enormous attention for its application to quantum sensing, encompassing the areas of not only physics and applied physics but also chemistry, biology and life sciences. Nonetheless, its key technical aspects can be understood from the viewpoint of magnetic resonance. We focus on three facets of this ever-expanding research field, to which our viewpoint is especially relevant: microwave engineering, materials science, and magnetometry. In explaining these aspects, we provide a technical basis and up-to-date technologies for the research on the NV centers.

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Interlayer Couplings Mediated by Antiferromagnetic Magnons. (arXiv:1802.07867v1 [cond-mat.mes-hall])

Fri, 2018-02-23 02:45

Collinear antiferromagnets (AFs) support two degenerate magnon excitations carrying opposite spin polarizations, by which magnons can function as electrons in spin transport. We explore the interlayer coupling mediated by antiferromagnetic magnons in an insulating ferromagnet (F)/AF/F trilayer structure. The internal energy of the AF depends on the orientations of the two Fs, which manifests as effective interlayer interactions JS1.S2 and K(S1.S2)^2. Both J and K are functions of temperature and the AF thickness. Interestingly, J is antiferromagnetic at low temperatures and ferromagnetic at high temperatures. In the high-temperature regime, J is estimated to be much larger than the interlayer dipole-dipole interaction, allowing direct experimental verification.

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Would quantum entanglement be increased by anti-Unruh effect?. (arXiv:1802.07886v1 [gr-qc])

Fri, 2018-02-23 02:45

We study the "anti-Unruh effect" for an entangled quantum state in reference to the counterintuitive cooling previously pointed out for an accelerated detector coupled to the vacuum. We show that quantum entanglement for an initially entangled (spacelike separated) bipartite state can be increased when either a detector attached to one particle is accelerated or both detectors attached to the two particles are in simultaneous accelerations. However, if the two particles (e.g., detectors for the bipartite system) are not initially entangled, entanglement cannot be created by the anti-Unruh effect. Thus, within certain parameter regime, this work shows that the anti-Unruh effect can be viewed as an amplification mechanism for quantum entanglement.

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Improving sensitivity to magnetic fields and electric dipole moments by using measurements of individual magnetic sublevels. (arXiv:1802.07892v1 [quant-ph])

Fri, 2018-02-23 02:45

We explore ways to use the ability to measure the populations of individual magnetic sublevels to improve the sensitivity of magnetic field measurements and measurements of atomic electric dipole moments (EDMs). When atoms are initialized in the $m=0$ magnetic sublevel, the shot-noise-limited uncertainty of these measurements is $1/\sqrt{2F(F+1)}$ smaller than that of a Larmor precession measurement. When the populations in the even (or odd) magnetic sublevels are combined, we show that these measurements are independent of the tensor Stark shift and the second order Zeeman shift. We discuss the complicating effect of a transverse magnetic field and show that when the ratio of the tensor Stark shift to the transverse magnetic field is sufficiently large, an EDM measurement with atoms initialized in the superposition of the stretched states can reach the optimal sensitivity.

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Longer distance continuous variable quantum key distribution protocol with photon subtraction at receiver. (arXiv:1802.07915v1 [quant-ph])

Fri, 2018-02-23 02:45

One of the limitation of continuous variable quantum key distribution is relatively short transmission distance of secure keys. In order to overcome the limitation, some solutions have been proposed such as reverse reconciliation, trusted noise concept, and non-Gaussian operation. In this paper, we propose a protocol using photon subtraction at receiver which utilizes synergy of the aforementioned properties. By simulations, we show performance of the proposed protocol outperforms other conventional protocols. We also find the protocol is more efficient in a practical case. Finally, we provide a guide for provisioning a system based on the protocol through an analysis for noise from a channel.

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Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory. (arXiv:1802.07939v1 [quant-ph])

Fri, 2018-02-23 02:45

We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of the time-independent Schroedinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via Supersymmetric Quantum Mechanics as well as to find a cornucopia of additional exact analytic solutions.

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A two-way quantum interface for linking $\text{Sr}^{\text{+}}$ transition at 422nm to the telecommunications C-band. (arXiv:1802.07947v1 [quant-ph])

Fri, 2018-02-23 02:45

We report a single-stage bi-directional interface capable of linking Sr$^+$ trapped ion qubits in a long-distance quantum network. Our interface converts photons between the Sr$^+$ emission wavelength at 422 nm and the telecoms C-band to enable low-loss transmission over optical fiber. We have achieved both up- and down-conversion at the single photon level with efficiencies of 9.4 $\%$ and 1.1 $\%$ respectively. Furthermore, we demonstrate that the noise introduced during the conversion process is sufficiently low to implement high-fidelity interconnects suitable for quantum networking.

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Quantum walks assisted by particle number fluctuations. (arXiv:1802.07952v1 [quant-ph])

Fri, 2018-02-23 02:45

We study the spreading of a quantum particle placed in a single site of a lattice or binary tree with the Hamiltonian permitting particle number changes. We show that the particle number-changing interactions accelerate the spreading beyond the ballistic expansion limit by inducing off-resonant Rabi oscillations between states of different numbers of particles. We consider the effect of perturbative number-changing couplings on Anderson localization in one-dimensional disordered lattices and show that they lead to decrease of localization. The effect of these couplings is shown to be larger at larger disorder strength, which is a consequence of the disorder-induced broadening of the particle dispersion bands.

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Entangled systems are unbounded sources of nonlocal correlations and of certified random numbers. (arXiv:1802.07962v1 [quant-ph])

Fri, 2018-02-23 02:45

The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities -- entanglement, non-locality and randomness -- relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: For systems in a given entangled state, how many nonlocal correlations in a sequence can we obtain by measuring them repeatedly? And from this generated sequence of non-local correlations, how many random numbers is it possible to certify? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from an entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.

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Topological phases of non-Hermitian systems. (arXiv:1802.07964v1 [cond-mat.mes-hall])

Fri, 2018-02-23 02:45

Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi-)edge modes. We then apply the K-theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a Z2 topological index for arbitrary quantum channels. Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.

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QuEST and High Performance Simulation of Quantum Computers. (arXiv:1802.08032v1 [quant-ph])

Fri, 2018-02-23 02:45

We introduce QuEST, the Quantum Exact Simulation Toolkit, and compare it to ProjectQ, qHipster and a recent distributed implementation of Quantum++. QuEST is the first open source, OpenMP and MPI hybridised, GPU accelerated simulator written in C, capable of simulating generic quantum circuits of general single-qubit gates and many-qubit controlled gates. Using the ARCUS Phase-B and ARCHER supercomputers, we benchmark QuEST's simulation of random circuits of up to 38 qubits, distributed over up to 2048 distributed nodes, each with up to 24 cores. We directly compare QuEST's performance to ProjectQ's on single machines, and discuss the differences in distribution strategies of QuEST, qHipster and Quantum++. QuEST shows excellent scaling, both strong and weak, on multicore and distributed architectures.

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Synchronizing the Smallest Possible System. (arXiv:1802.08036v1 [quant-ph])

Fri, 2018-02-23 02:45

We investigate the minimal Hilbert-space dimension for a system to be synchronized. We first show that qubits cannot be synchronized due to the lack of a limit cycle. Moving to larger spin values, we demonstrate that a single spin 1 can be phase-locked to a weak external signal of similar frequency and exhibits all the standard features of the theory of synchronization. Our findings rely on the Husimi Q representation based on spin coherent states which we propose as a tool to obtain a phase portrait.

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Renormalization Group Flow of the Aharonov-Bohm Scattering Amplitude. (arXiv:1802.08050v1 [hep-th])

Fri, 2018-02-23 02:45

The Aharonov-Bohm elastic scattering with incident particles described by plane waves is revisited by using the phase-shifts method. The formal equivalence between the cylindrical Schr\"odinger equation and the one-dimensional Calogero problem allows us to show that up to two scattering phase-shifts modes in the cylindrical waves expansion must be renormalized. The renormalization procedure introduces new length scales giving rise to spontaneous breaking of the conformal symmetry. The new renormalized cross-section has an amazing property of being non-vanishing even for a quantized magnetic flux, coinciding with the case of Dirac delta function potential. The knowledge of the exact beta function permits us to describe the renormalization group flows within the two-parametric family of renormalized Aharonov-Bohm scattering amplitudes. Our analysis demonstrates that for quantized magnetic fluxes a BKT-like phase transition at the coupling space occurs.

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Time-dependent nonlinear Jaynes-Cummings dynamics of a trapped ion. (arXiv:1802.08063v1 [quant-ph])

Fri, 2018-02-23 02:45

In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under con- sideration. In such complex scenarios, exact solutions of the dynamics are rarely available. Here we study the nonlinear vibronic dynamics of a trapped ion, driven in the resolved sideband regime with some small frequency mismatch. By describing the pump field in a quantized manner, we are able to derive exact solutions for the dynamics of the system. This eventually allows us to provide analytical solutions for various types of time-dependent quantities. In particular, we study in some detail the electronic and the motional quantum dynamics of the ion, as well as the time-evolution of the nonclassicality of the motional quantum state.

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What happens if measure the electron spin twice?. (arXiv:1802.08071v1 [physics.gen-ph])

Fri, 2018-02-23 02:45

The mainstream textbooks of quantum mechanics explains the quantum state collapses into an eigenstate in the measurement, while other explanations such as hidden variables and multi-universe deny the collapsing. Here we propose an ideal thinking experiment on measuring the spin of an electron with 3 steps. It is simple and straightforward, in short, to measure a spin-up electron in x-axis, and then in z-axis. Whether there is a collapsing predicts different results of the experiment. The future realistic experiment will show the quantum state collapses or not in the measurement.

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