Gaussian States Research Articles

Maximal entanglement increase with single-photon subtraction

Entanglement is an indispensable quantum resource for quantum information technology. In continuous-variable quantum optics, photon subtraction can increase the entanglement between Gaussian states of light, but for mixed states the extent of this entanglement increase is poorly understood. In this work, we use an entanglement measure based the Rényi-2 entropy to prove that single-photon subtraction increases bipartite entanglement by no more than log 2. This value coincides with the maximal amount of bipartite entanglement that can be achieved with one photon. The upper bound is valid for all Gaussian input states, regardless of the number of modes and the purity.

Accelerated Gaussian quantum state transfer between two remote mechanical resonators

The main challenge in deterministic quantum state transfer (QST) between remote mechanical resonators is the local decoherence and the transmission losses in the communication channel. In the path of overcoming this limitation, here we employ a shortcut to adiabatic passage protocol to devise a fast and reliable evolution path between two remote mechanical modes in separate optomechanical systems (OMSs). A QST between the two nodes is conceived by engineering their coupling to an intermediate fiber optical channel. The coupling pulses are operated such that the dark eigenmode of the system is decoupled from the fiber modes and transitions to the bright modes are compensated for by counterdiabatic drives. We show that one obtains a QST with high fidelity for various Gaussian states. The efficiency is compared to that of adiabatic passage (AP) protocol in the presence of losses and noises. Our results show that while the AP protocol is very sensitive to the decoherence, the shortcut to adiabaticity provides a robust and fast QST even for small values of the coupling strength. The performance of both protocols are also investigated for the case of multimode fiber through numerical and an effective single-model model which is found by the elimination of off-resonant fiber modes. Our findings may pave the way for using OMSs in the realization of continuous-variable Gaussian QST.

Extraction of SnO Subbandgap Defect Density by Numerical Modeling of p-Type TFTs

Recently, p-type tin monoxide (SnO) thin-film transistors (TFTs) have gained interest for all-oxide complementary metal–oxide semiconductor (CMOS) circuits for flexible electronics and back-end-of-line integration with Si. However, most SnO TFTs demonstrated so far exhibit a low on– off-current ratio and limited field effect mobility. To understand and improve SnO TFT performance, it is necessary to quantitatively characterize the subbandgap defects in SnO and at its dielectric interface. In this work, we establish numerical models which provide this understanding. By concurrent fitting of simulated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${I}_{\text{D}}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text{GS}}$ </tex-math></inline-formula> and effective mobility versus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}_{\text{GS}}$ </tex-math></inline-formula> to experimentally measured data, we can accurately extract SnO defect state profiles. Using the extracted simulation models, we then identify ways to improve SnO TFT performance. Specifically, a reduction in the density of shallow, bulk Gaussian acceptor states, is necessary to reduce the off-current, while reducing the contact resistance and interface donor-like tail state density can improve the SnO field effect mobility.

Magnetic moment invariant Gaussian states of a charged particle in a homogeneous magnetic field

Magnetic moment invariant Gaussian states of a charged particle in a homogeneous magnetic field

Computation of sandwiched relative α-entropy of two n-mode Gaussian states

A formula for the sandwiched relative [Formula: see text]-entropy [Formula: see text] for [Formula: see text], of two [Formula: see text]-mode Gaussian states [Formula: see text], [Formula: see text] in the boson Fock space [Formula: see text] is presented. This computation extensively employs the [Formula: see text]-parametrization of Gaussian states in [Formula: see text] introduced in Ref. 10.

Two-mode squeezed state quantisation and semiclassical portraits

Quantisation with Gaussian type states offers certain advantages over other quantisation schemes, in particular, they can serve to regularise formally discontinuous classical functions leading to well defined quantum operators. In this work we define a squeezed state quantisation in two dimensions using several families of squeezed states for one- and two-mode configurations. The completeness relations of the squeezed states are exploited in order to tackle the quantisation and semiclassical analysis of a constrained position dependent mass model with harmonic potential. The effects of the squeezing parameters on the resulting operators and phase space functions are studied, and configuration space trajectories are compared between the classical and semiclassical models.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

Estimation of the Wigner distribution of single-mode Gaussian states: A comparative study

In this work, we consider the estimation of single mode Gaussian states using four different measurement schemes namely: i) homodyne measurement, ii) sequential measurement, iii) Arthurs-Kelly scheme, and iv) heterodyne measurement, with a view to compare their relative performance. To that end, we work in the phase space formalism, specifically at the covariance matrix level, which provides an elegant and intuitive way to explicitly carry out involved calculations. We show that the optimal performance of the Arthurs-Kelly scheme and the sequential measurement is equal to the heterodyne measurement. While the heterodyne measurement outperforms the homodyne measurement in the mean estimation of squeezed state ensemble, the homodyne measurement outperforms the heterodyne measurement for variance estimation of squeezed state ensemble up to a certain range of squeezing parameter. We then modify the Hamiltonian in the Arthurs-Kelly scheme, such that the two meters can have correlations and show that the optimal performance is achieved when the meters are uncorrelated. We expect that the results will be useful in analyzing various quantum information and quantum communication protocols.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits.

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Observable bound for Gaussian illumination

We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical regime using a thermal state, a receiver implemented with a photon number difference measurement approaches its bound regardless of the signal mean photon number, while it asymptotically approaches the classical bound in the limit of a huge idler mean photon number.

Evolution of two-mode quantum states under a dissipative environment: Comparison of the robustness of squeezing and entanglement resources

We explore the relative robustness of single-mode squeezing and entanglement (which are quantum resources interconvertible via passive optics) for two-mode Gaussian states under different dissipative environments. When the individual modes interact with identical local baths, entanglement and squeezing decay at the same rate. However, when only one of the modes interacts with a local bath, the comparative robustness of entanglement and squeezing depends on the initial squeezing of the state. Similarly, when the system interacts with a global bath, the robustness of entanglement and squeezing depends on the initial squeezing. Thus depending on the nature of dissipative environments and the initial squeezing of the state, one can select the more robust form of resource out of squeezing and entanglement to store quantumness. This can be used to effectively enhance the performance of various quantum information processing protocols based on continuous variable Gaussian states.

Discord and decoherence

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of “quantum correlations” between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties.

Mode-selective single-photon addition to a multimode quantum field

Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion (PDC) processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the type-II collinear down conversion, while single-mode condition are retrieved for noncollinear type-I and type-II processes. Numerical results are shown for photon addition in PDC process at near-infrared and telecommunications wavelengths.

The semi-classical limit with a delta-prime potential

We consider the quantum evolution [Formula: see text] of a Gaussian coherent state [Formula: see text] localized close to the classical state [Formula: see text], where [Formula: see text] denotes a self-adjoint realization of the formal Hamiltonian [Formula: see text], with [Formula: see text] the derivative of Dirac’s delta distribution at [Formula: see text] and [Formula: see text] a real parameter. We show that in the semi-classical limit such a quantum evolution can be approximated (with respect to the [Formula: see text]-norm, uniformly for any [Formula: see text] away from the collision time) by [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] is a suitable self-adjoint extension of the restriction to [Formula: see text], [Formula: see text], of ([Formula: see text] times) the generator of the free classical dynamics. While the operator [Formula: see text] here utilized is similar to the one appearing in our previous work [C. Cacciapuoti, D. Fermi and A. Posilicano, The semi-classical limit with a delta potential, Ann. Mat. Pura Appl. 200 (2021) 453–489], in the present case the approximation gives a smaller error: it is of order [Formula: see text], [Formula: see text], whereas it turns out to be of order [Formula: see text], [Formula: see text], for the delta potential. We also provide similar approximation results for both the wave and scattering operators.

Mechanisms for the emergence of Gaussian correlations

We comprehensively investigate two distinct mechanisms leading to memory loss of non-Gaussian correlations after switching off the interactions in an isolated quantum system undergoing out-of-equilibrium dynamics. The first mechanism is based on spatial scrambling and results in the emergence of locally Gaussian steady states in large systems evolving over long times. The second mechanism, characterized as `canonical transmutation', is based on the mixing of a pair of canonically conjugate fields, one of which initially exhibits non-Gaussian fluctuations while the other is Gaussian and dominates the dynamics, resulting in the emergence of relative Gaussianity even at finite system sizes and times. We evaluate signatures of the occurrence of the two candidate mechanisms in a recent experiment that has observed Gaussification in an atom-chip controlled ultracold gas and elucidate evidence that it is canonical transmutation rather than spatial scrambling that is responsible for Gaussification in the experiment. Both mechanisms are shown to share the common feature that the Gaussian correlations revealed dynamically by the quench are already present though practically inaccessible at the initial time. On the way, we present novel observations based on the experimental data, demonstrating clustering of equilibrium correlations, analyzing the dynamics of full counting statistics, and utilizing tomographic reconstructions of quantum field states. Our work aims at providing an accessible presentation of the potential of atom-chip experiments to explore fundamental aspects of quantum field theories in quantum simulations.

A Gaussian Process State Space Model Fusion Physical Model and Residual Analysis for Fatigue Evaluation.

Residual stress is closely related to the evolution process of the component fatigue state, but it can be affected by various sources. Conventional fatigue evaluation either focuses on the physical process, which is limited by the complexity of the physical process and the environment, or on monitored data to form a data-driven model, which lacks a relation to the degenerate process and is more sensitive to the quality of the data. This paper proposes a fusion-driven fatigue evaluation model based on the Gaussian process state–space model, which considers the importance of physical processes and the residuals. Through state–space theory, the probabilistic space evaluation results of the Gaussian process and linear physical model are used as the hidden state evaluation results and hidden state change observation function, respectively, to construct a complete Gaussian process state–space framework. Then, through the solution of a particle filter, the importance of the residual is inferred and the fatigue evaluation model is established. Fatigue tests on titanium alloy components were conducted to verify the effectiveness of the fatigue evaluation model. The results indicated that the proposed models could correct evaluation results that were far away from the input data and improve the stability of the prediction.

Oscillator decomposition of infant fNIRS data.

The functional near-infrared spectroscopy (fNIRS) can detect hemodynamic responses in the brain and the data consist of bivariate time series of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) on each channel. In this study, we investigate oscillatory changes in infant fNIRS signals by using the oscillator decompisition method (OSC-DECOMP), which is a statistical method for extracting oscillators from time series data based on Gaussian linear state space models. OSC-DECOMP provides a natural decomposition of fNIRS data into oscillation components in a data-driven manner and does not require the arbitrary selection of band-pass filters. We analyzed 18-ch fNIRS data (3 minutes) acquired from 21 sleeping 3-month-old infants. Five to seven oscillators were extracted on most channels, and their frequency distribution had three peaks in the vicinity of 0.01-0.1 Hz, 1.6-2.4 Hz and 3.6-4.4 Hz. The first peak was considered to reflect hemodynamic changes in response to the brain activity, and the phase difference between oxy-Hb and deoxy-Hb for the associated oscillators was at approximately 230 degrees. The second peak was attributed to cardiac pulse waves and mirroring noise. Although these oscillators have close frequencies, OSC-DECOMP can separate them through estimating their different projection patterns on oxy-Hb and deoxy-Hb. The third peak was regarded as the harmonic of the second peak. By comparing the Akaike Information Criterion (AIC) of two state space models, we determined that the time series of oxy-Hb and deoxy-Hb on each channel originate from common oscillatory activity. We also utilized the result of OSC-DECOMP to investigate the frequency-specific functional connectivity. Whereas the brain oscillator exhibited functional connectivity, the pulse waves and mirroring noise oscillators showed spatially homogeneous and independent changes. OSC-DECOMP is a promising tool for data-driven extraction of oscillation components from biological time series data.

Quantum kernels with Gaussian state encoding for machine learning

Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that quantum-enhanced machine learning is closely related to kernel methods, where the exponentially large Hilbert space can be a feature space more expressive than classical ones. Here we investigate quantum kernel methods of encoding data into continuous-variable quantum states, with two newly introduced quantum kernels named squeezing amplitude kernel and coherent phase kernel from Gaussian state encoding, in which data is encoded as either in the amplitude or the phase. The kernels can be calculated on a quantum computer and then are combined with classical machine learning, e.g. support vector machine, for training and predicting tasks. Their comparisons with other classical kernels are also addressed. Lastly, we briefly discuss the universal approximation property of continuous-variable quantum kernels.

Modular Structure of the Weyl Algebra

We study the modular Hamiltonian associated with a Gaussian state on the Weyl algebra. We obtain necessary/sufficient criteria for the local equivalence of Gaussian states, independently of the classical results by Araki and Yamagami, Van Daele, Holevo. We also present a criterion for a Bogoliubov automorphism to be weakly inner in the GNS representation. The main application of our analysis is the description of the vacuum modular Hamiltonian associated with a time-zero interval in the scalar, massive, free QFT in two spacetime dimensions, thus complementing the recent results in higher space dimensions (Longo and Morsella in The massive modular Hamiltonian. arXiv:2012.00565). In particular, we have the formula for the local entropy of a one-dimensional Klein–Gordon wave packet and Araki’s vacuum relative entropy of a coherent state on a double cone von Neumann algebra. Besides, we derive the type {III}_1 factor property. Incidentally, we run across certain positive selfadjoint extensions of the Laplacian, with outer boundary conditions, seemingly not considered so far.

Erratum: Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors [Phys. Rev. A 100 , 052301 (2019)

Erratum: Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors [Phys. Rev. A <b>100</b> , 052301 (2019)