Showing papers in "Physical Review A in 2013"

Quantum computations without definite causal structure

Abstract: We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a predefined causal order. The simplest example of such a transformation is the classical switch of black boxes, where two input black boxes are arranged in two different orders conditionally on the value of a classical bit. The quantum version of this transformation---the quantum switch---produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure. Simulating these transformations in a circuit with fixed causal structure requires either postselection or an extra query to the input black boxes.

Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators

Abstract: We demonstrate that frequency (Kerr) comb generation in whispering-gallery-mode resonators can be modeled by a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatiotemporal model allows us to explore pulse formation in which a large number of modes interact cooperatively. Pulse formation is shown to play a critical role in comb generation, and we find conditions under which single pulses (dissipative solitons) and multiple pulses (rolls) form. We show that a broadband comb is the spectral signature of a dissipative soliton, and we also show that these solitons can be obtained by using a weak anomalous dispersion and subcritical pumping.

Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference

Abstract: Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.

Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases

Abstract: We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d + 1) mutually unbiased measurements in a classically simulated prepare-and-measure scheme and on a pair of entangled photons for dimensions ranging from d = 2 to 5. In our analysis, we pay attention to the detection efficiency and photon pair creation probability. As security measures, we determine from experimental data the average error rate, the mutual information shared between the sender and receiver, and the secret key generation rate per photon. We demonstrate that increasing the dimension leads to an increased information capacity as well as higher key generation rates per photon. However, we find that the benefit of increasing the dimension is limited by practical implementation considerations, which in our case results in deleterious effects observed beyond a dimension of d = 4.

Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter

Abstract: We present an ultrahigh-sensitivity gravimeter based on an ${}^{87}$Rb atom interferometer using stimulated Raman transitions. Compared with our previous work, a two-dimensional magneto-optical trap is added in the new gravimeter to increase the atom number and improve the detection signal-to-noise ratio, and a better optical phase-locked loop system is used to reduce the phase noise of Raman beams. Benefiting from these efforts and the excellent performance of the active vibration isolator, a short-term sensitivity of about 4.2 $\ensuremath{\mu}\text{Gal}/\sqrt{\text{Hz}}$ ($1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{Gal}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ $\text{m}/{\text{s}}^{2}$) is reached, which improves the sensitivity by a factor of 2 compared with the former best reported value. By a modulation experiment, we further indicate that the residual vibration noise contribution is about 1.2 $\ensuremath{\mu}\text{Gal}/\sqrt{\text{Hz}}$, which implies a possible improvement over the present absolute gravity measurement level by about one order of magnitude. Moreover, we demonstrate a calibration experiment to directly evaluate the sub-$\ensuremath{\mu}$Gal resolution of our gravimeter.

Coherent Ising machine based on degenerate optical parametric oscillators

Abstract: A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.

Self-Consistent Quantum Process Tomography

Abstract: Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors in tomography can not be fully corrected through oversampling or by performing a larger set of experiments. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner. The essential ingredient is to dene a likelihood function that assumes nothing about the gates used for preparation and measurement. In order to make the resulting optimization tractable we linearize about the target, a reasonable approximation when benchmarking a quantum computer as opposed to probing a black-box function.

Observation of Zitterbewegung in a spin-orbit-coupled Bose-Einstein condensate

Abstract: Spin-orbit-coupled ultracold atoms provide an intriguing new avenue for the study of rich spin dynamics in superfluids. In this Rapid Communication, we observe Zitterbewegung, the simultaneous velocity (thus position) and spin oscillations, of neutral atoms between two spin-orbit-coupled bands in a Bose-Einstein condensate (BEC) through sudden quantum quenches of the Hamiltonian. The observed Zitterbewegung oscillations are perfect on a short time scale but gradually damp out on a long time scale, followed by sudden and strong heating of the BEC. As an application, we also demonstrate how Zitterbewegung oscillations can be exploited to populate the upper spin-orbit band and observe a subsequent dipole motion. Our experimental results are corroborated by a theoretical and numerical analysis and showcase the great flexibility that ultracold atoms provide for investigating rich spin dynamics in superfluids.

Fisher information under decoherence in Bloch representation

Abstract: The dynamics of two variants of quantum Fisher information under decoherence is investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both sets of information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating-wave approximation. We further express the two information quantities in terms of the Bloch vector for a qudit by expanding the density matrix and Hermitian operators in a common set of generators of the Lie algebra $\text{su}(d)$. By calculating the dynamical quantum Fisher information, we find that the collisional dephasing significantly diminishes the precision of the phase parameter with the Ramsey interferometry.

Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

Abstract: We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional superconducting transmission line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super- and subradiance or to a coherent exchange-type interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms driven by a coherent state. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [van Loo (unpublished)].

Photon blockade in quadratically coupled optomechanical systems

Abstract: We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment.

Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations

Abstract: We use entropic uncertainty relations to formulate inequalities that witness Einstein-PodolskyRosen (EPR) steering correlations in diverse quantum systems. We then use these inequalities to formulate symmetric EPR-steering inequalities using the mutual information. We explore the diering natures of the correlations captured by one-way and symmetric steering inequalities, and examine the possibility of exclusive one-way steerability in two-qubit states. Furthermore, we show that steering inequalities can be extended to generalized positive operator valued measures (POVMs), and we also derive hybrid-steering inequalities between alternate degrees of freedom.

Preventing Calibration Attacks on the Local Oscillator in Continuous-Variable Quantum Key Distribution

Abstract: Establishing an information-theoretic secret key between two parties using a quantum key distribution (QKD) system is only possible when an accurate characterization of the quantum channel and proper device calibration routines are combined. Indeed, security loopholes due to inappropriate calibration routines have been shown for discrete-variable QKD. Here, we propose and provide experimental evidence of an attack targeting the local oscillator calibration routine of a continuous-variable QKD system. The attack consists in manipulating the classical local oscillator pulses during the QKD run in order to modify the clock pulses used at the detection stage. This allows the eavesdropper to bias the shot noise estimation usually performed using a calibrated relationship. This loophole can be used to perform successfully an intercept-resend attack. We characterize the loophole and suggest possible countermeasures.

Field-theoretical study of the Bose polaron

Abstract: We study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a non-self-consistent $T$-matrix approximation by comparing analytical results to numerical data obtained from a fully self-consistent $T$-matrix approach. The latter takes into account an infinite number of bosons excited from the condensate.

Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling

Abstract: We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.

Geometric quantum discord through the Schatten 1-norm

Abstract: It has recently been pointed out that the geometric quantum discord, as defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum correlations, since it may increase under local reversible operations on the unmeasured subsystem. Here, we revisit the geometric discord by considering general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm able to define a consistent quantum correlation measure. In addition, by restricting the optimization to the tetrahedron of two-qubit Bell-diagonal states, we provide an analytical expression for the 1-norm geometric discord, which turns out to be equivalent to the negativity of quantumness. We illustrate the measure by analyzing its monotonicity properties.

Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits

Abstract: We perform a proof-of-principle demonstration of the measurement-device-independent quantum key distribution protocol using weak coherent states and polarization-encoded qubits over two optical fiber links of 8.5 km each. Each link was independently stabilized against polarization drifts using a full-polarization control system employing two wavelength-multiplexed control channels. A linear-optics-based polarization Bell-state analyzer was built into the intermediate station, Charlie, which is connected to both Alice and Bob via the optical fiber links. Using decoy states, a lower bound for the secret-key generation rate of 1.04$\ifmmode\times\else\texttimes\fi{}$10${}^{\ensuremath{-}6}$ bits/pulse is computed.

Geometrical characterization of non-Markovianity

Abstract: We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples.

Arbitrarily large steady-state bosonic squeezing via dissipation

Abstract: We discuss how large amounts of steady-state quantum squeezing (beyond 3 dB) of a mechanical resonator can be obtained by driving an optomechanical cavity with two control lasers with differing amplitudes. The scheme does not rely on any explicit measurement or feedback, nor does it simply involve a modulation of an optical spring constant. Instead, it uses a dissipative mechanism with the driven cavity acting as an engineered reservoir. It can equivalently be viewed as a coherent feedback process, obtained by minimally perturbing the quantum nondemolition measurement of a single mechanical quadrature. This shows that in general the concepts of coherent feedback schemes and reservoir engineering are closely related. We analyze how to optimize the scheme, how the squeezing scales with system parameters, and how it may be directly detected from the cavity output. Our scheme is extremely general, and could also be implemented with, e.g., superconducting circuits.

Contextuality in measurement-based quantum computation

Abstract: We show, under natural assumptions for qubit systems, that measurement-based quantum computations (MBQCs) which compute a nonlinear Boolean function with a high probability are contextual The class of contextual MBQCs includes an example which is of practical interest and has a superpolynomial speedup over the best-known classical algorithm, namely, the quantum algorithm that solves the ``discrete log'' problem

Low-overhead constructions for the fault-tolerant Toffoli gate

Abstract: We present two constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T=\mathrm{exp}(i\ensuremath{\pi}{\ensuremath{\sigma}}^{z}/8)$ gates, whereas conventional circuits require seven $T$ gates. An extension of this result is that adding $n$ control inputs to a controlled gate requires $4n$ $T$ gates, whereas the best prior result was $8n$. The second contribution is a quantum circuit for the Toffoli gate which can detect a single ${\ensuremath{\sigma}}^{z}$ error occurring with probability $p$ in any one of eight $T$ gates required to produce the Toffoli gate. By postselecting circuits that did not detect an error, the posterior error probability is suppressed to lowest order from $4p$ (or $7p$, without the first contribution) to $28{p}^{2}$ for this enhanced construction. In fault-tolerant quantum computing, this construction can reduce the overhead for producing logical Toffoli gates by an order of magnitude.

Process verification of two-qubit quantum gates by randomized benchmarking

Abstract: We implement a complete randomized benchmarking protocol on a system of two superconducting qubits. The protocol consists of randomizing over gates in the Clifford group, which experimentally are generated via an improved two-qubit cross-resonance gate implementation and single-qubit unitaries. From this we extract an optimal average error per Clifford operation of $0.0936$. We also perform an interleaved experiment, alternating our optimal two-qubit gate with random two-qubit Clifford gates, to obtain a two-qubit gate error of $0.0653$. We compare these values with a two-qubit gate error of $\ensuremath{\sim}0.12$ obtained from quantum process tomography, which is likely limited by state preparation and measurement errors.

Postprocessing for quantum random number generators: entropy evaluation and randomness extraction

Abstract: Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.

Topological invariance and global Berry phase in non-Hermitian systems

Abstract: By studying the topological invariance and Berry phase in non-Hermitian systems, we reveal the basic properties of the complex Berry phase and generalize the global Berry phases $Q$ to identify the topological invariance for non-Hermitian systems. We find that $Q$ can identify topological invariance in two kinds of non-Hermitian model, the two-level non-Hermitian Hamiltonian and the bipartite dissipative model. For the bipartite dissipative model, an abrupt change of the Berry phase in the parameter space reveals a quantum phase transition and is related to the exceptional points. These results give the basic relationships between the Berry phase and the quantum and topological phase transitions of non-Hermitian systems.

Quantum circuits of T-depth one

Abstract: We give a $\text{Clifford}+T$ representation of the Toffoli gate of $T$-depth one, using four ancillas. More generally, we describe a class of circuits whose $T$-depth can be reduced to one by using sufficiently many ancillas. We show that the cost of adding an additional control to any controlled gate is at most eight additional $T$ gates and $T$-depth two. We also show that the circuit $THT$ does not possess a $T$-depth one representation with an arbitrary number of ancillas initialized to $|0\ensuremath{\rangle}$.

Condition for macroscopic realism beyond the Leggett-Garg inequalities

Abstract: In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this paper, we discuss another necessary condition called no-signaling in time. It solely bases on comparing the probability distribution for a macrovariable at some time for the cases where previously a measurement has or has not been performed. Although the concept is analogous to the no-signaling condition in the case of Bell tests, it can be violated according to quantum mechanical predictions even in situations where no violation of Leggett-Garg inequalities is possible.

Past of a quantum particle

Abstract: Although there is no consensus regarding the ``reality'' of the past of a quantum particle, in situations where there is only one trajectory with a nonvanishing quantum wave of the particle between its emission and detection points, it seems ``safe'' to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and postselected particles. Examples in which this method contradicts the above common sense description of the past of the particle are presented. It is argued that it is possible to describe the past of a quantum particle, but the naive approach has to be replaced by both forward- and backward-evolving quantum states.

Quantum Fisher information of entangled coherent states in the presence of photon loss

Abstract: We investigate the performance of entangled coherent states for quantum-enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

Abstract: We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number $N$ of atoms. For finite $N$, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any $N$ and correctly captures the atoms' depolarization due to dissipative dephasing.

Scattering of ultracold molecules in the highly resonant regime

Abstract: Compared to purely atomic collisions, ultracold molecular collisions potentially support a much larger number of Fano-Feshbach resonances due to the enormous number of rovibrational states available. In fact, for alkali-metal dimers we find that the resulting density of resonances cannot be resolved at all, even on the sub-$\ensuremath{\mu}$K temperature scale of ultracold experiments. As a result, all observables become averaged over many resonances and can effectively be described by simpler, nonresonant scattering calculations. Two particular examples are discussed: nonchemically reactive RbCs and chemically reactive KRb. In the former case, the formation of a long-lived collision complex may lead to the ejection of molecules from a trap. In the latter case, chemical reactions broaden the resonances so much that they become unobservable.