Gaussian States Research Articles

Violation of Bell inequalities by stochastic simulations of Gaussian States based on their positive Wigner representation

At first sight, the use of an everywhere positive Wigner function as a probability density to perform stochastic simulations in quantum optics seems equivalent to the introduction of local hidden variables, thus preventing any violation of Bell inequalities. However, because of the difference between symmetrically and normally ordered operators, some trajectories in stochastic simulations can imply negative intensities, despite a positive mean. Hence, Bell inequalities do not apply. Here, we retrieve for a weakly squeezed Gaussian state the maximum violation on polarization states allowed by quantum mechanics, for the Clauser-Horn-Shimony-Holt (CHSH), as well as for the Clauser-Horn Bell inequalities. For the case of the Clauser-Horn Bell inequality, the influence of the quantum efficiency of the detectors is studied, and for both inequalities, the influence of the degree of squeezing is assessed, as well as the uncertainty range versus the number of trajectories used in the simulations.

The semiclassical limit on a star-graph with Kirchhoff conditions

We consider the dynamics of a quantum particle of mass m on a n-edges star-graph with Hamiltonian H_K=-(2m)^{-1}hbar ^2 Delta and Kirchhoff conditions in the vertex. We describe the semiclassical limit of the quantum evolution of an initial state supported on one of the edges and close to a Gaussian coherent state. We define the limiting classical dynamics through a Liouville operator on the graph, obtained by means of Kreĭn’s theory of singular perturbations of self-adjoint operators. For the same class of initial states, we study the semiclassical limit of the wave and scattering operators for the couple (H_K,H_{D}^{oplus }), where H_{D}^{oplus } is the Hamiltonian with Dirichlet conditions in the vertex.

A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications

Let Γ(H) be the boson Fock space over a finite dimensional Hilbert space H. It is shown that every Gaussian symmetry admits a Klauder–Bargmann integral representation in terms of coherent states. Furthermore, Gaussian states, Gaussian symmetries, and second quantization contractions belong to a weakly closed self-adjoint semigroup E2(H) of bounded operators in Γ(H). This yields a common parametrization for these operators. It is shown that the new parametrization for Gaussian states is a fruitful alternative to the customary parametrization by position–momentum mean vectors and covariance matrices. This leads to a rich harvest of corollaries: (i) every Gaussian state ρ admits a factorization ρ=Z1†Z1, where Z1 is an element of E2(H) and has the form Z1=cΓ(P)exp∑r=1nλrar+∑r,s=1nαrsaras on the dense linear manifold generated by all exponential vectors, where c is a positive scalar, Γ(P) is the second quantization of a positive contractive operator P in H, ar, 1 ≤ r ≤ n, are the annihilation operators corresponding to the n different modes in Γ(H), λr∈C, and [αrs] is a symmetric matrix in Mn(C); (ii) an explicit particle basis expansion of an arbitrary mean zero pure Gaussian state vector along with a density matrix formula for a general Gaussian state in terms of its E2(H)-parameters; (iii) a class of examples of pure n-mode Gaussian states that are completely entangled; (iv) tomography of an unknown Gaussian state in Γ(Cn) by the estimation of its E2(Cn) parameters using O(n2) measurements with a finite number of outcomes.

Heat exchange and fluctuation in Gaussian thermal states in the quantum realm

The celebrated exchange fluctuation theorem—proposed by Jarzynski and Wójcik (2004 Phys. Rev. Lett. 92 230602) for heat exchange between two systems in thermal equilibrium at different temperatures—is explored here for quantum Gaussian states in thermal equilibrium. We employ the Wigner distribution function formalism for quantum states, which exhibits a close resemblance to the classical phase-space trajectory description, to arrive at a formal Jarzynski–Wójcik result. For two Gaussian states in thermal equilibrium at two different temperatures kept in contact with each other for a fixed duration of time, we show that the Jarzynski–Wójcik-like relation reduces to the corresponding classical result in the limit ℏ → 0.

Charged complexity and the thermofield double state

We establish a systematic framework for studying quantum computational complexity of Gaussian states of charged systems based on Nielsen’s geometric approach. We use this framework to examine the effect of a chemical potential on the dynamics of complexity. As an example, we consider the complexity of a charged thermofield double state constructed from two free massive complex scalar fields in the presence of a chemical potential. We show that this state factorizes between positively and negatively charged modes and demonstrate that this fact can be used to relate it, for each momentum mode separately, to two uncharged thermofield double states with shifted temperatures and times. We evaluate the complexity of formation for the charged thermofield double state, both numerically and in certain analytic expansions. We further present numerical results for the time dependence of complexity. We compare various aspects of these results to those obtained in holography for charged black holes.

Gaussian Process State-Space Models with Time-Varying Parameters and Inducing Points.

We propose time-varying Gaussian process state-space models (TVGPSSM) whose hyper-parameters vary with time. The models have the ability to estimate time-varying functions and thereby increase flexibility to extract information from observed data. The proposed inference approach makes use of time-varying inducing points to adapt to changes of the function, and it exploits hierarchical importance sampling. The experimental results show that the approach has better performance than that of the standard Gaussian process.

Decay and recurrence of non-Gaussian correlations in a quantum many-body system

Gaussian models provide an excellent effective description of many quantum many-body systems ranging from condensed-matter systems1,2 all the way to neutron stars3. Gaussian states are common at equilibrium when the interactions are weak. Recently it was proposed that they can also emerge dynamically from a non-Gaussian initial state evolving under non-interacting dynamics4,5,6,7,8,9,10,11. Here we present the experimental observation of such a dynamical emergence of Gaussian correlations in a quantum many-body system. This non-equilibrium evolution is triggered by abruptly switching off the effective interaction between the observed collective degrees of freedom, while leaving the interactions between the microscopic constituents unchanged. Starting from highly non-Gaussian correlations, consistent with the sine–Gordon model12, we observe a Gaussian state emerging over time as revealed by the decay of the fourth- and sixth-order connected correlations in the quantum field. A description of this dynamics requires a novel mechanism for the emergence of Gaussian correlations, which is relevant for a wide class of quantum many-body systems. In our closed system with non-interacting effective degrees of freedom, we do not expect full thermalization13,14,15,16,17,18,19. This memory of the initial state is confirmed by observing recurrences20 of non-Gaussian correlations.

Linear open quantum systems with passive Hamiltonians and a single local dissipative process

We consider linear open quantum systems with passive Hamiltonians and a single, local dissipative process. Generally speaking, these systems are easier to implement than systems with active Hamiltonians and non-local dissipative processes. We parametrize the set of all covariance matrices corresponding to pure Gaussian steady states that can be achieved by this type of quantum system. Given such pure states, we parametrize the corresponding linear quantum systems with passive Hamiltonians and a single, local dissipative process that generate them.

Quantifying the Efficiency of State Preparation via Quantum Variational Eigensolvers

Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as the quantum approximate optimization algorithm (QAOA). While it has been numerically shown that such algorithms prepare certain correlated states of quantum spins with surprising accuracy, a systematic way of quantifying the efficiency of the QAOA in general classes of models has been lacking. Here, we propose that the success of the QAOA in preparing ordered states is related to the interaction distance of the target state, which measures how close that state is to the manifold of all Gaussian states in an arbitrary basis of single-particle modes. We numerically verify this for several examples of nonintegrable quantum models, including Ising models with two- and three-spin interactions and the cluster model in an external field. Our results suggest that the structure of the entanglement spectrum, as witnessed by the interaction distance, correlates with the success of QAOA state preparation, and that this correlation also contains information about different phases present in the model. We conclude that the QAOA typically finds a solution that perturbs around the closest free-fermion state.2 MoreReceived 3 August 2020Accepted 8 December 2020DOI:https://doi.org/10.1103/PRXQuantum.2.010309Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement measuresOptimization problemsQuantum controlTechniquesIsing modelQuantum InformationCondensed Matter, Materials & Applied Physics

Dissipative Engineering of Gaussian Entangled States in Harmonic Lattices with a Single-Site Squeezed Reservoir.

We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes nontrivial multipartite entangled states such as cluster states suitable for measurement-based quantum computation.

Continuous-variable quantum cryptography with discrete alphabets: Composable security under collective Gaussian attacks

We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we provide a composable security analysis in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.

Entanglement renormalization for gauge invariant quantum fields

The continuous multiscale entaglement renormalization ansatz (cMERA) [Haegeman et al., Phys. Rev. Lett., 110, 100402 (2013)] is a variational wavefunctional for ground states of quantum field theories. So far, only scalar bosons and fermions have been considered. In this paper we explain how to generalize the cMERA framework to gauge invariant quantum fields. The fundamental difficulty to be addressed is how to make the gauge constraints (local linear constraints in the Hilbert space) compatible with the UV structure of the cMERA wavefunctional (which is generated by a quasi-local entangler). For simplicity, we consider $U(1)$ gauge theory in $d+1$ spacetime dimensions, a non-interacting theory with massless Hamiltonian $H_{U(1)}$ and Gaussian scale invariant ground state $|\Psi_{U(1)}\rangle$. We propose a gauge invariant cMERA wavefunctional $|\Psi^{\Lambda}_{U(1)}\rangle$ that, by construction, accurately reproduces the long distance properties of $|\Psi_{U(1)}\rangle$ while remaining somewhat unentangled at short distances. Moreover, $|\Psi^{\Lambda}_{U(1)}\rangle$ is the exact ground state of a gauge invariant, local Hamiltonian $H^{\Lambda}_{U(1)}$ whose low energy properties coincide with those of $H_{U(1)}$. Our construction also extends the cMERA formalism to massive (non-gauge invariant) vector boson quantum fields.

Generation of optical Schrödinger cat states by generalized photon subtraction

We propose a high-rate generation method of optical Schr\"odinger cat states. Thus far, photon subtraction from squeezed vacuum states has been a standard method in cat-state generation, but its constraints on experimental parameters limit the generation rate. In this paper, we consider the state generation by photon number measurement in one mode of two-mode Gaussian states, which is a generalization of conventional photon subtraction, and derive the conditions to generate high-fidelity and large-amplitude cat states. Our method relaxes the constraints on experimental parameters, allowing us to optimize them and attain a high generation rate. Supposing realistic experimental conditions, the generation rate of cat states with large amplitudes ($|\ensuremath{\alpha}|\ensuremath{\ge}2)$ can exceed megacounts per second, about ${10}^{3}$ to ${10}^{6}$ times better than typical rates of conventional photon subtraction. This rate would be improved further by the progress of related technologies. The ability to generate non-Gaussian states at a high rate is important in quantum computing using optical continuous variables, where scalability has been demonstrated but preparation of non-Gaussian states of light remains as a challenging task for universality and fault tolerance. Our proposal reduces the difficulty of the state preparation and opens a way for practical applications in quantum optics.

Continuous-variable quantum key distribution based on photon addition operation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11664017 and 11964013) and the Training Program for Academic and Technical Leaders of Major Disciplines in Jiangxi Province, China (Grant No. 20204BCJL22053).

It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution (CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source. It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.

Effect of plasma oxidation on tin-oxide active layer for thin-film transistor applications

In this study, the plasma oxidation effect in tin-oxide (SnOx) thin film was investigated. And on this basis, we fabricated n-type thin-film transistors (TFTs) using the SnOx thin film with the plasma oxidation by experiments. By adjusting the processing time of the oxygen plasma treatment (OPT), the optimized SnOx TFT device exhibited an extremely high field-effect mobility of 87.6 cm2 V−1 s−1, a desirable on-to-off current ratio of 1.9 × 104 and a threshold voltage of − 0.9 V. Furthermore, we investigated the origin of the performance enhancements in the n-type SnOx TFTs with the optimized OPT by introducing the density of states (DOS) modeling in TCAD simulation. The numerical simulation indicated that the attributes of donor-like Gaussian defect states (oxygen vacancies) were modified in overall DOS due to the plasma oxidation effect. These present results show that the SnOx TFT treated by oxygen plasma has great promise in the future high-performance flat panel display industries.

Purification complexity without purifications

We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric (QFIM) on the space of density matrices as the complexity measure. Due to Uhlmann’s theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.

P-Type Cu2O Thin Film Transistors for Active Matrix Displays: Physical Modeling and Numerical Simulation

In this paper, we present the physical modeling and numerical simulations of p-type Cu2O TFT for the design and development of active matrix displays. In Cu2O, the carrier transport is through copper and oxygen vacancies (VCu and VO) which are prominent defects due to their low formation energies. These defects were modeled with acceptor-like and donor-like Gaussian states. From the simulations, it was observed that the VCu significantly controls the OFF current and threshold voltage (Vth), while VO degrades the ON current. For the analysis of device stability, both positive and negative bias stress (PBS and NBS) on Cu2O TFT was investigated with dielectric/channel interface traps in simulations. Under NBS, a significant negative shift in the Vth was observed due to hole trapping from channel to dielectrics. On the contrary, during PBS, a small shift in Vth was observed with significant degradation in sub-threshold swing (SS) due to the deficiency of free electron and the presence of additional defects generated in Cu2O channel as stress time increase. In addition to this effect of increase in Cu2O channel thickness were studied where a significant amount of shift in Vth from -7.1 V to -6.1 V was observed as the thickness increased from 45 nm to 65 nm. Finally, the dynamic performance of Cu2O was evaluated and found to be better for higher channel thickness in terms of holding of the output voltage. From these observations, the p-type Cu2O TFT shall be considered for the stable and efficient pixel circuit of active matrix displays such as AMLCD.

Estimating a fluctuating magnetic field with a continuously monitored atomic ensemble

We study the problem of estimating a time dependent magnetic field by continuous optical probing of an atomic ensemble. The magnetic field is assumed to follow a stochastic Ornstein-Uhlenbeck process and it induces Larmor precession of the atomic ground state spin, which is read out by the Faraday polarization rotation of a laser field probe. The interactions and the measurement scheme are compatible with a hybrid quantum-classical Gaussian description of the unknown magnetic field, and the atomic and field variables. This casts the joint conditional quantum dynamics and classical parameter estimation problem in the form of update formulas for the first and second moments of the classical and quantum degrees of freedom. Our hybrid quantum-classical theory is equivalent with the classical theory of Kalman filtering and with the quantum theory of Gaussian states. By reference to the classical theory of smoothing and with the quantum theory of past quantum states, we show how optical probing after time $t$ improves our estimate of the value of the magnetic field at time $t$, and we present numerical simulations that analyze and explain the improvement over the conventional filtering approach.

Squeezing as a resource to counteract phase diffusion in optical phase estimation

We address a phase estimation scheme using Gaussian states in the presence of non-Gaussian phase noise. At variance with previous analysis, we analyze situations in which the noise occurs before encoding phase information. In particular, we study how squeezing may be profitably used before or after phase diffusion. Our results show that squeezing the probe after the noise greatly enhances the sensitivity of the estimation scheme, as witnessed by the increase of the quantum Fisher information. We then consider a realistic setup where homodyne detection is employed at the measurement stage, and address its optimality as well as its performance in the two different scenarios.

A flexible robust Student's t-based multimodel approach with maximum Versoria criterion

The performance of the state estimation for Gaussian state space models can be degraded if the models are affected by the non-Gaussian process and measurement noises with uncertain degree of non-Gaussianity. In this paper, we propose a flexible robust Student's t-based multimodel approach. More specifically, the degrees of freedom parameter from the Student's t-distribution is assumed unknown and modelled by a Markov chain of state values. In order to capture more information of the Student's t-distributions propagated through multiple models, we establish a model-based Versoria cost function in the form of a weighted mixture rather than the original form, and maximize the function to interact and fuse the multiple models. Simulated results prove the flexibility of the robustness of the proposed Student's t-basedmultimodel approach when the existence probability of the outliers is uncertain.