Author(s): Muzzamal I. Shaukat, Eduardo V. Castro, and Hugo Terças

We study the finite time entanglement dynamics between two dark-soliton qubits due to quantum fluctuations in quasi-one-dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long lifetime. We explore the entanglement...

[Phys. Rev. A 98, 022319] Published Thu Aug 16, 2018

Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting feature in this scenario, when the quantum discord of Alice's qubits increases, then the quantum discord of Bob's prepared qubits decreases. Furthermore, we show that the fidelity of one-qubit quantum teleportation using Bob's prepared qubits as the channel is higher than using Alice's qubits.

Measures to quantify the flow of quantum information and its sensitivity to environment perturbations are needed to better understand the evolution of open quantum systems and to distinguish non-Markovian from Markovian dynamics. Here, we show that the extent of correlations in many-body quantum systems is an experimentally accessible metric for quantifying the spread of quantum information. Our experiment applies multiple-quantum nuclear magnetic resonance (NMR) technique to take snapshots of the multi-spin correlations between a central spin and the spins in its surrounding environment. We argue that the width of the distribution of these multi-spin correlations is the natural metric for quantifying the flow of information between the system and the environment. Quantum information shared between the two is sensitive to environment perturbations. The out-of-time-order correlation function (OTOC) is used to measure this sensitivity. By analyzing the decay of the OTOC as a function of our metric instead of time, we demonstrate the exponential behavior of the OTOC.

Phase transitions at a finite (i.e. non-zero) temperature are typically dominated by classical correlations, in contrast to zero temperature transitions where quantum mechanics plays an essential role. Therefore, it is natural to ask if there are any signatures of a finite temperature phase transition in measures that are sensitive only to quantum correlations. Here we study one such measure, namely, entanglement negativity, across finite temperature phase transitions in several exactly solvable Hamiltonians and find that it is a singular function of temperature across the transition. As an aside, we also calculate the entanglement of formation exactly in a related, interacting model.

The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in $\hbar^2$ that is exponentially increasing with time within an intermediate time-window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature.

We investigate a superconducting circuit consisting of multiple capacitively-coupled charge qubits. The collective Rabi oscillation of qubits is numerically studied in detail by imitating environmental fluctuations according to the experimental measurement. For the quantum circuit composed of identical qubits, the energy relaxation of the system strongly depends on the interqubit coupling strength. As the qubit-qubit interaction is increased, the system's relaxation rate is enhanced firstly and then significantly reduced. In contrast, the inevitable inhomogeneity caused by the nonideal fabrication always accelerates the collective energy relaxation of the system and weakens the interqubit correlation. However, such an inhomogeneous quantum circuit is an interesting test bed for studying the effect of the system inhomogeneity in quantum many-body simulation.

In this work, we establish a connection between nonlinear electronic spectroscopy and quantum information protocols for the non-disturbance condition. The non-fulfillment of the later is a witness of nonclassicality. Our approach permits us to express the non-disturbance condition in terms of common observables in the context of electronic spectroscopy experiments, such as the induced polarization. We then provide the theoretical framework allowing one to infer nonclassicality from the detected signals in these experiments. A prominent feature of our proposal is then the model independence. In particular, for third-order nonlinear spectroscopies, such as the widely used two-dimensional electronic spectroscopy, we find that the induction of third-order polarization in systems satisfying inversion symmetry automatically implies nonclassicality.

We present the optimal design for an on-chip single-photon source based on spontaneous four-wave mixing in a system of coupled ring microresonators, which provides frequency uncorrelated joint spectral amplitude of the biphoton field and thereby generation of pure single-photon heralded states. A simple method is proposed for suppressing negative dispersion effects by optimizing the controlled spectroscopic parameters of the system. It shown that the optimal coupling parameters, in combination with the optimal spectral width of the pump pulse, give rise to the highest purity of the heralded photons for a given pump linewidth.

In this paper we design quantum algorithms for studying the autocorrelation spectrum of a Boolean function and its individual coefficients. Informally, the autocorrelation coefficient of a Boolean function f() at some point a measures the average correlation among the values f(x) and f(x xor a). The Walsh spectrum is a related concept that is well-studied primarily due to its connection to the quantum circuit for the Deutsch-Jozsa problem but the autocorrelation spectrum has not received similar attention that we attempt to deliver in this paper.

We propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First and foremost, we give an algorithm that samples from the Walsh spectrum of any derivative of f(); the derivative of a Boolean function is an extension of autocorrelation to correlation among multiple values of f(). Using a relation between the 1st-order derivative and the autocorrelation coefficients, we design an algorithm to sample the input points according to squares of the autocorrelation coefficients. Then we given a different set of algorithms for estimating the square of a particular coefficient or cumulative sum of their squares. Our last algorithm combines the technique of amplitude estimation and amplification in a novel manner to find points with high values of autocorrelation coefficients.`

The recent direct experimental measurement of quantum entanglement paves the way towards a better understanding of many-body quantum systems and their correlations. Nevertheless, the overall majority of both the experimental and theoretical advances had so far been limited to bosonic systems. Here, we study fermionic systems. Using experimental setups where multiple copies of the same state are prepared, arbitrary order R\'{e}nyi entanglement entropies and entanglement negativities can be extracted by utilizing spatially-uniform beam splitters and on-site occupation measurement which are attainable using current experimental settings. We illustrate how our paradigm could be used for experimental quantum simulations of fermions on manifolds with nontrivial spin structures.

Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation, and the conserved current satisfies the corresponding conservation equation.

Quantum sensors, such as the Nitrogen Vacancy (NV) color center in diamond, are known for their exquisite sensitivity, but their performance is degraded by noise. To improve the long-term robustness of a quantum sensor, here we realize an integrated combinatorial spin sensor in the same micrometer-scale footprint, which exploits two different spin sensitivity to distinct physical quantities to stabilize one spin sensor with local information collected in realtime via the second sensor. We show that we can use the electronic spins of a large ensemble of NV centers as sensor of the local magnetic field fluctuations, affecting both spin sensors, in order to stabilize the output signal of interleaved Ramsey sequences performed on the 14N nuclear spin. An envisioned application of such a device is to sense rotation rates with a stability of several days, allowing navigation with limited or no requirement of geo-localization. Our results would enable stable rotation sensing for over several hours, which already reflects better performance than MEMS gyroscopes of comparable sensitivity and size.

The realization of topological quantum phases of matter remains a key challenge to condensed matter physics and quantum information science. In this work, we demonstrate that progress in this direction can be made by combining concepts of tensor network theory with Majorana device technology. Considering the topological double semion string-net phase as an example, we exploit the fact that the representation of topological phases by tensor networks can be significantly simpler than their description by lattice Hamiltonians. The building blocks defining the tensor network are tailored to realization via simple units of capacitively coupled Majorana bound states. In the case under consideration, this defines a remarkably simple blueprint of a synthetic double semion string-net, and one may be optimistic that the required device technology will be available soon. Our results indicate that the implementation of tensor network structures via mesoscopic quantum devices may define a powerful novel avenue to the realization of synthetic topological quantum matter in general.

Quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We develop the BFGS algorithm to study the corresponding optimization problem in quantum Boltzmann machine, especially focus on the target states being a family of states with parameters. As an typical example, we study the target states being the real symmetric two-qubit pure states, and we find two obvious features shown in the numerical results on the minimal quantum relative entropy: First, the minimal quantum relative entropy in the first and the third quadrants is zero; Second, the minimal quantum relative entropy is symmetric with the axes $y=x$ and $y=-x$ even with one qubit hidden layer. Then we theoretically prove these two features from the geometric viewpoint and the symmetry analysis. Our studies show that the traditional physical tools can be used to help us to understand some interesting results from quantum Boltzmann machine learning.

An attractive implementation for quantum cryptography is the continuous variable variation, as it relies on standard telecommunication components. Modulating the quantum signal using a Gaussian format is attractive since it has been proven to be secure. This work investigates the effect of the roll-off of a root raised cosine pulse shaping and matched filter on the excess noise performance of a Gaussian modulated quantum key distribution system in a simulated back to back configuration. Contrary to intuition, it is found that the roll-off parameter does not significantly impact the performance of the system.

Most of the matter-wave interferometry (MWI) schemes for quantum sensing are so far evaluated in ideal situations without noises. In this work, we provide assessments of generic multiqubit MWI schemes under realistic dephasing noises. We find that for certain classes of the MWI schemes, the use of entangled probes could be detrimental to the optimal precision. This result challenges the conventional wisdom that entanglement can enhance the precision in quantum metrology. We initiate the analyses by investigating the optimal precision of multiqubit Sagnac atom interferometry for rotation sensing. And we show that due to the competition between the unconventional interrogation-time quadratic phase accumulation and the exponential dephasing processes, the Greenberger-Horne-Zeilinger (GHZ) state, which is the optimal input state in noiseless scenarios, gives even worse precision than its uncorrelated counterpart. Then our assessments are further extended to generic MWI schemes for quantum sensing with entangled states and under decoherence. Finally, a quantum error-correction logical GHZ state is tentatively analyzed, which could have the potential to recover the Heisenberg scaling and improve the sensitivity.

We propose a protocol for quantum networking based on deterministic quantum state transfer between distant memory nodes using photon-number superposition states (PNSS). In the suggested scheme, the quantum nodes are single atoms confined in high-finesse optical cavities linked by photonic channels. The quantum information written in a superposition of atomic Zeeman states of sending system is faithfully mapped through cavity-assisted Raman scattering onto PNSS of linearly polarized cavity photons. The photons travel to the receiving cavity, where they are coherently absorbed with unit probability creating the same superposition state of the second atom, thus ensuring high-fidelity transfer between distant nodes. We develop this approach at first for photonic qubit and show that this superposition state is no less reliably protected against the propagation losses compared to the single-photon polarization states, whereas the limitation associated with the delivery of more than one photon does not affect the process fidelity. Then, by preserving the advantages of qubits, we extend the developed technique to the case of state transfer by photonic qutrit, which evidently possesses more information capacity. This reliable and efficient scheme promises also a successful distribution of entanglement over long distances in quantum networks.

The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock. We consider what happens when this classical time is replaced by a non-relativistic quantum-mechanical description of the clock. From the clock-dependent Schr\"odinger equation (as analogue of the time-dependent Schr\"odinger equation) we derive a continuity equation, where, instead of a time-derivative, an operator occurs that depends on the flux (probability current) density of the clock. This clock-dependent continuity equation can be used to analyze the dynamics of a quantum system and to study degrees of freedom that may be used as internal clocks for an approximate description of the dynamics of the remaining degrees of freedom. As an illustration, we study a simple model for coupled electron-nuclear dynamics and interpret the nuclei as quantum clock for the electronic motion. We find that whenever the Born-Oppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons.

We use tensor network methods - Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks - to simulate the one dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.

We introduce a mechanism for light-induced Floquet engineering of the Fermi surface to dynamically tip the balance between competing instabilities in correlated condensed matter systems in the vicinity of a van-Hove singularity. We first calculate how the Fermi surface is deformed by an off-resonant, high-frequency light field and then determine the impact of this deformation on the ordering tendencies using an unbiased functional renormalization group approach. As a testbed, we investigate Floquet engineering in cuprates driven by light. We find that the $d$-wave superconducting ordering tendency in this system can be strongly enhanced over the Mott insulating one. This gives rise to extended regions of induced $d$-wave superconductivity in the effective phase diagram in the presence of a light field.