The concept of steering was introduced by Schrödinger in 1935 as a generalization the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and measurements one party. Until now, it has never been rigorously defined, so not known (for example) what mixed are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner isotropic states) that strict subset states, superset Bell nonlocality. For...

Modern cavity quantum electrodynamics (cavity QED) illuminates the most fundamental aspects of coherence and decoherence in mechanics. Experiments on atoms cavities can be described by elementary models but reveal intriguing subtleties interplay coherent dynamics with external couplings. Recent activity this area has pioneered powerful new approaches to study fueled growth information science. In years come, purview QED will continue grow as researchers build a rich infrastructure attack...

The motion of individual cesium atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM). A single atom moving within generates large variations in transmission a weak probe laser, which are recorded real time. An inversion algorithm then allows trajectories to be reconstructed from record cavity and reveals bound orbit by mechanical forces associated photons. In these initial experiments, ACM yields 2-micrometer spatial resolution 10-microsecond time...

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show finding optimal is essentially equivalent the shortest path between two points in certain curved geometry. By recasting problem of as geometric problem, we open up possibility using mathematical techniques Riemannian geometry suggest new algorithms, or prove limitations on power computers.

We present a formulation of feedback in quantum systems which the best estimates dynamical variables are obtained continuously from measurement record, and fed back to control system. apply this method problem cooling confining single degree freedom, compare it current schemes signal is directly manner usually considered existing treatments feedback. Direct may be combined with by estimation, resulting combination, performed on linear system, closely analogous classical LQG theory residual

In a recent work [Phys. Rev. Lett. 98, 140402 (2007)] we defined ``steering,'' type of quantum nonlocality that is logically distinct from both nonseparability and Bell nonlocality. the bipartite setting, it hinges on question whether Alice can affect Bob's state at distance through her choice measurement. More precisely operationally, Alice, with classical communication, convince Bob they share an entangled under circumstances trusts nothing says. We argue if she can, then this demonstrates...

We introduce a family of separability criteria that are based on the existence extensions bipartite quantum state \ensuremath{\rho} to larger number parties satisfying certain symmetry properties. It can be easily shown all separable states have required extensions, so nonexistence such an extension for particular implies is entangled. One main advantages this approach searching cast as convex optimization problem known semidefinite program. Whenever does not exist, dual constructs explicit...

We introduce and discuss the problem of quantum feedback control in context established formulations classical theory, examining conceptual analogies essential differences. describe application state-observer based laws, familiar to systems apply our methods particular case switching state a particle double-well potential.

We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest these tests corresponds the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and more complicated are strictly stronger. new tractable due powerful computational theoretical methods for class convex optimization problems known as semidefinite programs. successfully applied results many low-dimensional states literature where PPT test fails. As a...

We present an experimental demonstration of the power feedbackin quantum metrology, confirming predicted [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] superior performanceof adaptive homodyne technique for single-shotmeasurement optical phase. For measurements performed on weak coherentstates with no prior knowledge signal phase, homodyneestimation approaches closer to intrinsic uncertaintythan any previous technique. Our results underscore importanceof real-time feedback reaching limits...

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles both error correction and feedback control. Our uses continuous measurements Hamiltonian operations, which are weaker control tools than typically assumed correction. develop cost function appropriate use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study the three-qubit bit-flip code in detail demonstrate can improve fidelity of...

Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because system's Hilbert space grows exponentially with number constituent particles, N. Fortunately, it still possible to investigate a when state system possesses sufficient symmetry. In this paper, we present practical method for efficiently computing various bipartite measures states symmetric subspace and perform these calculations $N\ensuremath{\sim}{10}^{3}.$ By considering all splits,...

We report the dispersive charge-state readout of a double quantum dot in few-electron regime using situ gate electrodes as sensitive detectors. benchmark this gate-sensing technique against well established point contact (QPC) charge detector and find comparable performance with bandwidth 10 MHz an equivalent sensitivity 6.3 x 10-3 e/ \sqrt Hz. Dispersive alleviates burden separate detectors for systems promises to enable qubits scaled-up arrays.

The purpose of this paper is to develop a synthesis theory for linear dynamical quantum stochastic systems that are encountered in optics and phenomenological models circuits. In particular, such will enable the systematic realization coherent/fully controllers control, amongst other potential applications. We show how general can be constructed by assembling an appropriate interconnection one degree freedom open harmonic oscillators and, setting, discuss network approximately synthesized or...

Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence is the primary obstacle establishing scalable information processing architecture. Strategies such as environmental materials engineering, error correction dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in qubit using real-time Hamiltonian parameter estimation. Using rapidly converging Bayesian approach, precisely measure...

Over the past decade we have seen an explosion of demonstrations quantum coherence in atomic, optical, and condensed matter systems.These developments placed a new emphasis on production robust optimal control techniques presence environmental noise.We discuss use dynamical decoupling as form open-loop capable suppressing effects dephasing coherent systems.We introduce concept pulse-sequence construction filter-design problem, making connections with filter design from theory electrical...

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground an infinite one-dimensional (1D) system. It does this by embedding sites into ``environment'' chain, allowing to relax and then merging them with environment in order refine approximation. By making use operators, our approach able directly model any long-range interaction that can be systematically approximated series decaying exponentials. We apply these techniques compute...

Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, parametric amplification is relatively accessible, but previously thought limited 3dB squeezing in steady state. We consider effect applying continuous weak measurement and feedback this system. If drive optimally detuned from resonance, correlations between quadratures unlimited steady-state squeezing. Compared back-action evasion, we demonstrate that strength,...

Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform gates via measurements on such would be insensitive small variations in Hamiltonian. Here, we describe class symmetry-protected topological orders one-dimensional systems, any one which ensures perfect operation identity gate. As result, robust property an entire phase lattice, when protected by appropriate symmetry.

We imagine an experiment on unknown quantum mechanical system in which the is prepared various ways and a range of measurements are performed. For each measurement $M$ preparation $\ensuremath{\rho}$ experimenter can determine, given enough time, probability outcome $a$: $p(a\ensuremath{\mid}M,\ensuremath{\rho})$. How large does Hilbert space have to be order allow us find density matrices operators that will reproduce distribution? In this paper, we prove simple lower bound for dimension...

We study the quantum moment problem: given a conditional probability distribution together with some polynomial constraints, does there exist state rho and collection of measurement operators such that (i) obtaining particular outcome when is performed on specified by distribution, (ii) satisfy constraints. For example, constraints might specify must commute. show if an instance problem unsatisfiable, then exists certificate form proving this. Our proof based recent result in algebraic...

Many proposals for quantum information processing are subject to detectable loss errors. In this Letter, we show that topological error correcting codes, which protect against computational errors, also extremely robust losses. We present analytical results showing the maximum tolerable rate is 50%, determined by square-lattice bond percolation threshold. This saturates bound set no-cloning theorem. Our numerical support and a graceful trade-off between thresholds

Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these using randomized benchmarking now routine. However, direct comparison between measured thresholds complicated by fact estimates average while reflect worst-case behavior when gate used as part of large computation. These two measures can differ orders magnitude in regime interest. Here we facilitate experimentally accessible quantities arise current...

We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization an atomic force microscope cantilever, achieved by optimal estimation, is enhanced up 6.2 in one position quadrature when detuned drive used. This is, principle, limited only oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides pathway achieve robust quantum below zero-point motion. Broadly, our results demonstrate that...