Neural quantum propagators for driven-dissipative quantum dynamics

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.

The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti-normally ordered moments of photon creation and annihilation operators, the set of which contains complete information on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and thermalization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrodinger cat states).

Time fractional evolution of a single quantum state and entangled state

The Laser Interferometric Gravitational-Wave Observatory (LIGO) is designed to detect the Gravitational Waves (GW) predicted by Albert Einstein’s general theory of relativity. The advanced LIGO project is ongoing an upgrade to increase the detection sensitivity by more than a factor of 10, which will make the events detection a routine occurrence. In addition to using higher power lasers, heavier test mass, and better isolation systems, several new designs and techniques are proposed in the long-term upgrade, such as modifying the optics configuration to reduce the quantum noise, active noise cancellation of the Newtonian noise, optimizing the coating structure, and employing non-Guassian laser beams etc. In the first part of my thesis (Chapters 2 and 3), I apply statistical mechanics and elastostatics to the LIGO coated mirrors, and study the thermal fluctuations that dominate advanced LIGO’s most sensitive frequency band from 40 Hz to 200 Hz. In particular, in Chapter 2, I study the so-called coating Brownian noise, fluctuations of mirrors coated with multiple layers of dielectrics due to internal friction. Assuming coating materials to be isotropic and homogeneous, I calculate the cross spectra of Brownian fluctuations in the bulk and shear strains of the coating layers, as well as fluctuations in the height of the coating-substrate interface. The additional phase shifting and back-scattering caused by photo elastic effects are also considered for the first time. In Chapter 3, I study whether it is realistic to adopt higher-order Laguerre-Gauss modes in LIGO, in order to mitigate the effect of mirror thermal noise. We investigate the effect on the detector’s contrast defect caused by the mode degeneracy. With both analytical calculation and numerical simulation, we show that with this approach, the detector’s susceptibility to mirror figure errors is reduced greatly compared to using the nondegenerate modes, therefore making it unacceptable for LIGO requirements. For the future GW detectors, with much lower noises and higher sensitivity, this might be used to investigate the quantum behaviors of macroscopic mechanical objects. In recent years the linear optomechanical systems with cavity modes coupling to a mechanical oscillator have been studied extensively. In the second part of my thesis (Chapter 4), I study the interaction between a single photon and a high-finesse cavity with a movable mirror, in the so-called strong coupling regime, where the recoil of the photon can cause significant change in the momentum of the mirror. The results are applied to analyze the case with a Fabry-Perot cavity. We also present that with engineering the photon wave function, it is possible to prepare the oscillator into an arbitrary quantum state.

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function (representing a pure state) but by a density matrix (representing a mixed state). I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research.

Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message

Quantum gyroscopes have the advantages of high precision and drift-free, and are extensively applied in high accuracy spacecraft attitude control, but it is extremely sensitive to quantum noise, zero-bias drift and nonlinear errors under complex space conditions, which directly affect the accuracy of attitude solving. According to the well-established quantum gyro error models, including the random walk model and Markov error modeling, We propose a multi-channel error physics model, which integrates the non-Gaussian error modeling, multi-scale quantum state perturbation analysis and sensor-environment interaction coupling mechanism (MCEAM-AKF). In this section we use the error propagation equation to obtain the response matrix as influenced by noise under the evolution of quantum state, not only the noise responses of device linear part but also the nonlinear terms of state transition, which is the internal state decoherence phenomenon of the device. Then a model and augmented state based adaptive Kalman filter algorithm is designed, which integrates the time-varying error covariance estimation mechanism and the multi-layer scale observation update strategy and achieves the real-time dynamic correction of the attitude angle output error. Furthermore, external reference sources (e.g., star sensors) for closed-loop joint calibration accordingly to the movements to enhance the anti-interference ability and fast convergence performance are introduced in the model. Simulation results demonstrate that the average attitude angle error of MCEAM-AKF model can be decreased by $38.2 \%$ for different orbit and disturbance scenarios.

Density matrix of a quantum field in a particle-creating background

Quantum state reconstruction, or state reconstruction for short, aims at identifying an unknown quantum state ( states in quantum mechanics) on the basis of experimentally accessible data. The Quantum Optics community usually refers to this inverse problem as quantum (state) tomography while the expression quantum state estimation is often used in the field of Quantum computation. Reconstruction procedures depend on the physical context defined by the system carrying the unknown state, the experimentally accessible observables, the size of the ensemble of systems prepared in the unknown state, and the precision of the measured data. A two-level system (such as a spin-1/2, a qubit, or the two polarizations of a photon) prepared in a state with density matrix ρ is sufficient to illustrate the idea of state reconstruction. With two non-negative eigenvalues summing to one, the density matrix is a positive operator, and it depends on three real parameters. In the Bloch representation, the parameters combine to a real vector n with length |n| 1,

The first part of the chapter is devoted to the discussion of density operators. We first introduce the definition of a density operator and the unitary evolution of a quantum state. We then examine the measurement of a quantum system using the density operator approach. We present the density operator associated with a qubit and a harmonic oscillator at thermal equilibrium. The second part of the chapter focuses on bipartite systems. We show that the quantum state of a subsystem is given by the partial trace of the density operator of the global system. Finally, we explain the concept of purification of a density operator

Trainable parameterized quantum encoding and application based on enhanced robustness and parallel computing

Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify arbitrary multipartite pure quantum states using adaptive local projective measurements. Moreover, we establish a universal upper bound on the sample complexity that is independent of the local dimensions. Numerical calculations further indicate that Haar-random pure states can be verified with a constant sample cost, irrespective of the qudit number and local dimensions, even in the adversarial scenario in which the source cannot be trusted. As alternatives, we provide several simpler variants that can achieve similar high efficiencies without using Schmidt decomposition. The simplest variant consists of only two distinct tests.

The topological features of a heavy‐mass hole (HH) confined in a 2D Si quantum well system via Bloch sphere (BS) representation and logic gate analysis are studied. Strong anisotropy‐and‐nonparabolicity in the semiconductor valence band causes the re‐degeneracy between HHs having opposite spins. The newly yielded degenerate states function as topological singularities. By employing the semiclassical equation of cyclotron motion, the time‐evolved (TE) Schrödinger equation as a rate equation is rewritten, and then the numerically solved TE wave function on the BS by determining the zenith and azimuthal angles is represented. The two‐state rotating‐wave (TSRW) approximation introduced reveals that the slope of against quantum state (time) evolution includes the information of the non‐Abelian Berry connection. The TSRW further demonstrates that the slope of contains the information of the Abelian connection. The TE operator is expressed by the three rotation logic gates around the x‐axis by an angle , which is sandwiched by the two rotations and around the BS pole axis (z). The TSRW approach enables us to decompose into two partial rotations around the z‐axis, with Abelian and non‐Abelian Berry connections.

We laser-cool single beryllium ions in a Paul trap to the ground (n equals 0) quantum harmonic oscillator state with greater than 90% probability. From this starting point, we can put the atom into various quantum states of motion by application of optical and rf electric fields. Some of these states resemble classical states (the coherent states), while others are intrinsically quantum, such as number states or squeezed states. We have created entangled position and spin superposition states (Schrodinger cat states), where the atom's spatial wavefunction is split into two widely separated wave packets. We have developed methods to reconstruct the density matrices and Wigner functions of arbitrary motional quantum states. These methods should make it possible to study decoherence of quantum superposition states and the transition from quantum to classical behavior. Calculations of the decoherence of superpositions of coherent states are presented.

There exists an interesting relationship between entanglement and the time evolution of composite quantum systems: quantum entanglement enhances the ‘speed’ of evolution of certain quantum states, as measured by the time needed to reach an orthogonal state. Previous research done on this subject has been focused upon comparing extreme cases (highly entangled states versus separable states) or upon bi-partite systems. In the present contribution we explore the aforementioned connection (between entanglement and time evolution) in the cases of two-qubits and N-qubits systems, taking into account states of intermediate entanglement. In particular, we investigate a family of energetically symmetric states of low entanglement that saturate the quantum speed bound. We show that, as the number of qubits increases, very little entanglement is needed to reach the quantum speed limit.