The resource theory of quantum coherence studies the off-diagonal elements a density matrix in distinguished basis, whereas purity all deviations from maximally mixed state. We establish direct connection between two theories, by identifying as maximal which is achievable unitary operations. states that saturate this maximum identify universal family coherent states. These are optimal resources under incoherent operations, and thus independent way quantified. For distance-based quantifiers...

This paper shows that signals with a specific spatial dependence can be directly measured quadratic quantum advantage by preparing appropriate states utilize entanglement between sensors, hence the measurement process is not affected other signals, including noise, different dependence.

We report a proof-of-principle experimental demonstration of the quantum speed-up for learning agents utilizing small-scale information processor based on radiofrequency-driven trapped ions. The decision-making process agent within projective simulation paradigm machine is implemented in system two qubits. latter are realized using hyperfine states frequency-addressed atomic ions exposed to static magnetic field gradient. show that deliberation time this quadratically improved with respect...

Zusammenfassung Die Quantenschlüsselverteilung ist eine der fortschrittlichsten Quantentechnologien. Entsprechende Komponenten sind kommerziell erhältlich. Ihr Einsatz auf Satelliten und in vielen Demonstrationsnetzen wird weltweit erprobt. Allerdings benötigen die bisher meist verwendeten Verfahren „vertrauenswürdige“ Zwischenstationen, etwa Satelliten. Weltweit arbeiten viele Forschungsgruppen daran, mit globaler Reichweite zu entwickeln, ohne diese speziellen möglicherweise...

Using trapped atomic ions we demonstrate a tailored and versatile effective spin-system suitable for quantum simulations universal computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system thus serve as memory, while simultaneously, other coupled perform conditional dynamics. Also, pulses change sign of spin-spin couplings, well their strength, even during course algorithm. Taking advantage simultaneous long-range coupling between three...

The dynamics of cellular mechanisms can be investigated through the analysis networks. One simplest but most popular modeling strategies involves logic-based models. However, these models still face exponential growth in simulation complexity compared with a linear increase nodes. We transfer this approach to quantum computing and use upcoming technique field simulate resulting Leveraging logic has many benefits, including reduction algorithms for systems biology tasks. To showcase...

Novel ion traps that provide either a static or dynamic magnetic gradient field allow for the use of radio-frequency radiation coupling internal and motional states ions, which is essential conditional quantum logic. We show Hamiltonian describing this in presence resonant gradient, identical, dressed state basis, to case gradient. The strength both cases described by same effective Lamb-Dicke parameter. This insight can be used overcome demanding experimental requirements when using...

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding factors and illustrate this factorization scheme various examples. This algorithm relies solely on interference scales exponentially.

The complementarity of a single photon's particlelike and wavelike behaviors can be described by the inequality ${D}^{2}+{V}^{2}\ensuremath{\le}1$, with $D$ being path distinguishability $V$ fringe visibility. In this paper, we generalize duality relation to multiphoton case, where two concepts, higher-order visibility, are introduced quantify multiphotons.

We develop a general theory to estimate magnetic field gradients in quantum metrology. consider system of $N$ particles distributed on line whose internal degrees freedom interact with field. Usually gradient estimation is based precise measurements the at two different locations, performed independent groups particles. This approach, however, sensitive fluctuations offset determining level splitting and results collective dephasing. In this work, we use framework metrology assess maximal...

In order to faithfully detect the state of an individual two-state quantum system (qubit) realized using, for example, a trapped ion or atom, selective scattering resonance fluorescence is well established.The simplest way read out this measurement and assign threshold method.The detection error can be decreased by using more advanced methods like time-resolved method [1] π-pulse [2].These were introduced qubits with single possible change during process.However, there exist many hyperfine...

Quantum metrology is one of the technologies from which we expect a quantum superiority over classical strategies in near future. For single-parameter estimation, clear advantage for global based on entanglement can be proven. However, there exist different answers to question whether are better than separable multi-parameter estimation. The putative inconsistency investigation problem settings as well interpretations word 'separable' leading estimation strategies. In this paper, discuss...

We present a unified approach to different recent entanglement criteria. Although they were developed in ways, we show that are all applications of more general principle given by the Cauchy-Schwarz inequality. explain this and how use it derive not only already known criteria, but also criteria which unknown so far. systematically investigate its potential limitations detect bipartite multipartite entanglement. Furthermore, describe apply our generalized detection scheme find measurement...

We propose three implementations of the Gauss sum factorization schemes discussed in part I this series (Wölk et al 2011 New J. Phys. 13 103007): (i) a two-photon transition multi-level ladder system induced by chirped laser pulse, (ii) one-photon two-level atom with periodically modulated excited state and (iii) linearly driven sequence ultrashort pulses. For each these quantum systems, we show that excitation probability amplitude is given an appropriate sum. provide rules on how to encode...

We investigate phase and frequency estimation with different measurement strategies under the effect of collective noise. First, we consider standard linear scheme present an experimentally realizable optimization initial probe states by rotations. identify optimal rotation angle for times. Second, show that subshot noise sensitivity---up to Heisenberg limit---can be reached in presence using differential interferometry, where one part system is used monitor For this, not only...

We report a detailed investigation on near-ground state cooling of one and two trapped atomic ions. introduce simple sideband method for confined atoms ions, using RF radiation applied to bare ionic states in static magnetic field gradient, demonstrate its application ions at secular trap frequencies, ωz≈2π×117 kHz. For single 171Yb+ ion, the cycle reduces average phonon number, n from Doppler limit n= 0.30(12). This is agreement with theoretically estimated lowest achievable number this...

Abstract We consider non-local sensing of scalar signals with specific spatial dependence in the Bayesian regime. design schemes that allow one to achieve optimal scaling and are immune noise sources a different than signal. This is achieved by using sensor array spatially separated sensors constructing multi-dimensional decoherence free subspace. While Fisher regime sharp prior multiple measurements only spectral range Δ important, single-shot broad number available energy levels L crucial....

Abstract In recent years, quantum-enhanced machine learning has emerged as a particularly fruitful application of quantum algorithms, covering aspects supervised, unsupervised and reinforcement learning. Reinforcement offers numerous options how theory can be applied, is arguably the least explored, from perspective. Here, an agent explores environment tries to find behavior optimizing some figure merit. Some first approaches investigated settings where this exploration sped-up, by...

Factorization of numbers with the help Gauss sums relies on an intimate relationship between maxima these functions and factors. Indeed, when we restrict ourselves to integer arguments sum profit from a one-to-one relationship. As result identification factors by is unique. However, for non-integer such as rational this powerful instrument find breaks down. We develop new strategies factoring using at arguments. This approach may application in recent suggestion factor light interferometer...

In the last decade quantum machine learning has provided fascinating and fundamental improvements to supervised, unsupervised reinforcement learning. learning, a so-called agent is challenged solve task given by some environment. The learns exploring environment exploiting rewards it gets from For classical environments, such as deterministic strictly epochal an analogue can be constructed which allows find quadratically faster applying algorithms. this paper, we analytically analyze...

We propose two algorithms to factor numbers using Gauss sums and entanglement: (i) in a Shor-like algorithm we encode the standard sum one of entangled states (ii) an interference create superposition probability amplitudes states.These schemes are rather efficient provided that there exists fast can detect period function hidden its zeros.

The size of controllable quantum systems has grown in recent times. Therefore, the spatial degree freedom becomes more and important experimental systems. However, investigation entanglement many-body mainly concentrated on number entangled particles ignored so far. As a consequence, general concept together with experimentally realizable criteria been missing to describe distribution entanglement. We close this gap by introducing width as measure develop detect based solely global...

The center-of-mass position of a single trapped atomic ion is measured and tracked in time with high precision. Employing near-resonant radio frequency field wavelength 2.37 cm static magnetic gradient 19 T/m, the spatial location determined an unprecedented wavelength-relative resolution 5 $\times$ 10$^{-9}$, corresponding to absolute precision 0.12 nm. Measurements electrostatic force on demonstrate sensitivity 2.2 10$^{-23} ~\text{N}/\sqrt{\text{Hz}}$. real-time measurement atom's...