Experimental quantum state tomography via compressed sampling

A fundamental difficulty in demonstrating quantum state tomography is that the required resources grow exponentially with the system size. For pure states and nearly pure states, the task of tomography can be more efficient. We proposed two methods for state reconstruction, by (1) minimizing entropy and (2) maximizing likelihood. The algorithm of compressed sampling is employed to solve the optimization problem. Experiments are demonstrated considering 4-qubit photonic states. The results show that (1) much fewer measurements than the standard tomography are sufficient to obtain high fidelity, and (2) the method of maximizing likelihood is more accurate and noise robust than the original reconstruction method of compressed sampling. Furthermore, the physical meaning of the methods of minimizing entropy and maximizing likelihood is clear.     

Quantum state tomography and fidelity estimation via Phaselift

Experiments of multi-photon entanglement have been performed by several groups. Obviously, an increase on the photon number for fidelity estimation and quantum state tomography causes a dramatic increase in the elements of the positive operator valued measures (POVMs), which results in a great consumption of time in measurements. In practice, we wish to obtain a good estimation of fidelity and quantum states through as few measurements as possible for multi-photon entanglement. Phaselift provides such a chance to estimate fidelity for entangling states based on less data. In this paper, we would like to show how the Phaselift works for six qubits in comparison to the data given by Pan’s group, i.e., we use a fraction of the data as input to estimate the rest of the data through the obtained density matrix, and thus goes beyond the simple fidelity analysis. The fidelity bound is also provided for general Schrödinger Cat state. Based on the fidelity bound, we propose an optimal measurement approach which could both reduce the copies and keep the fidelity bound gap small. The results demonstrate that the Phaselift can help decrease the measured elements of POVMs for six qubits. Our conclusion is based on the prior knowledge that a pure state is the target state prepared by experiments.     

Quantum state and process tomography via adaptive measurements

We investigate quantum state tomography(QST) for pure states and quantum process tomography(QPT) for unitary channels via adaptive measurements. For a quantum system with a d-dimensional Hilbert space, we first propose an adaptive protocol where only 2d. 1 measurement outcomes are used to accomplish the QST for all pure states. This idea is then extended to study QPT for unitary channels, where an adaptive unitary process tomography(AUPT) protocol of d2+d.1measurement outcomes is constructed for any unitary channel. We experimentally implement the AUPT protocol in a 2-qubit nuclear magnetic resonance system. We examine the performance of the AUPT protocol when applied to Hadamard gate, T gate(/8 phase gate), and controlled-NOT gate,respectively, as these gates form the universal gate set for quantum information processing purpose. As a comparison, standard QPT is also implemented for each gate. Our experimental results show that the AUPT protocol that reconstructing unitary channels via adaptive measurements significantly reduce the number of experiments required by standard QPT without considerable loss of fidelity.     

基于压缩感知超分辨鬼成像

分辨率是成像系统的一个重要参数, 获得高分辨率图像一直是鬼成像系统的一个目标. 本文提出了以成像系统点扩散函数作为先验知识, 基于稀疏测量的超分辨压缩感知鬼成像重建模型. 搭建了一套计算鬼成像实验装置, 用于验证该模型对于提高鬼成像系统分辨率的有效性, 并与传统的鬼成像计算模型进行了对比. 实验表明, 利用该模型可突破成像系统衍射极限分辨率的限制, 得到超分辨鬼成像. 关键词： 鬼成像 压缩感知 超分辨 稀疏测量     

Quantum state tomography of dissociating molecules

Using tomographic reconstruction we determine the complete internuclear quantum state, represented by the Wigner function, of a dissociating I2 molecule based on femtosecond time resolved position and momentum distributions of the atomic fragments. The experimental data are recorded by timed ionization of the photofragments with an intense 20 fs laser pulse. Our reconstruction method, which relies on Jaynes's maximum entropy principle, will also be applicable to time resolved position or momentum data obtained with other experimental techniques.     

Quantum state tomography with array detectors

I propose a method for measuring the quantum state of an optical field that occupies a mode having a complicated spatial structure. The technique uses array detectors and a single, plane-wave local oscillator beam. The advantage of using array detectors is that the local oscillator is not mode matched to the field being measured, yet the deleterious effects of this mismatch on the effective detection efficiency are greatly reduced compared to using single detectors. Indeed, when the spatial mode of the signal field is describable by a real function, the effective mode-matching efficiency is unity.     

Quantum state tomography for generic pure states

We examine the problem of whether a multipartite pure quantum state can be uniquely determined by its reduced density matrices.We show that a generic pure state in three party Hilbert space HA■HB■HC, where dim(HA) = 2 and dim(HB) = dim(HC), can be uniquely determined by its reduced states on subsystems HA■HB and HA■HC. Then, we generalize the conclusion to the case that dim(H_1) 2. As a corollary, we show that a generic N-qudit pure quantum state is uniquely determined by only two of its[(N+1)/2]-particle reduced density matrices. Furthermore,our results indicate a method to uniquely determine a generic N-qudit pure state of dimension D = d~N with only O(D) local measurements, which is an improvement compared to the previous known approach that uses O(D log~2 D) or O(D log D) local measurements.     

Quantum state reconstruction via continuous measurement

We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state, new information is continually mapped onto the measured observable. A Bayesian filter is then used to update the state estimate in accordance with the measurement record. This generalizes the standard paradigm for quantum tomography based on strong, destructive measurements on separate ensembles. This approach to state estimation induces minimal perturbation of the measured system, giving information about observables whose evolution cannot be described classically in real time and opening the door to new types of quantum feedback control.     

Quantum state preparation via asymptotic completeness

We demonstrate that any quantum state |chi> of a single mode radiation field can be prepared with arbitrarily high fidelity by interaction with a sequence of two-level atoms, prepared in a suitable initial state. No final state measurement of the atoms is needed.     

Quantum state transfer via adiabatic passage

Based on adiabatic passage, we propose a scheme for implementing the quantum transfer of an unknown atomic state. In our scheme, we utilize photons for ideal quantum transmission between two cavities with the successful probability being about 1. Meanwhile, the scheme is robust against the effects of atomic spontaneous emission. It may be useful for transferring quantum information among spatially distant atoms.     

Causal MRI reconstruction via Kalman prediction and compressed sensing correction

This technical note addresses the problem of causal online reconstruction of dynamic MRI, i.e. given the reconstructed frames till the previous time instant, we reconstruct the frame at the current instant. Our work follows a prediction-correction framework. Given the previous frames, the current frame is predicted based on a Kalman estimate. The difference between the estimate and the current frame is then corrected based on the k-space samples of the current frame; this reconstruction assumes that the difference is sparse. The method is compared against prior Kalman filtering based techniques and Compressed Sensing based techniques. Experimental results show that the proposed method is more accurate than these and considerably faster.     

Quantum homodyne tomography of a two-photon Fock state

We present a continuous-variable experimental analysis of a two-photon Fock state of free-propagating light. This state is obtained from a pulsed nondegenerate parametric amplifier, which produces two intensity-correlated twin beams. Counting two photons in one beam projects the other beam in the desired two-photon Fock state, which is analyzed by using a pulsed homodyne detection. The Wigner function of the measured state is clearly negative. We developed a detailed analytic model which allows a fast and efficient analysis of the experimental results.     

Quantum state tomography of an itinerant squeezed microwave field

We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a preamplifier to improve the quantum efficiency of the field quadrature measurement from 2% to 36%±4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 68(-7)(+9)% of the variance of the vacuum. We reconstruct the state's density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.     

Quantum state engineering in ion-traps via adiabatic passage

We propose two relatively robust schemes to generate entangled W states of three (or generally N) ions in ion trap systems by using adiabatic passage technique and appropriately designed ion-field couplings in a single step. In the first scheme, we apply the N-pod fractional stimulated Raman adiabatic passage (F-STIRAP) technique to generate W state of N ions using two Gaussian laser pulses. We also show that the W state of N ? 1 ions can be created via a simple N-pod standard STIRAP by two laser pulses. In the second scheme, we generate the entangled state of N ions via ??-pulse technique by a single laser pulse. We also study the population transfer of the system by numerical solutions of the master equation, considering the effect of decoherence channels due to laser intensity fluctuations and dissipation in the phonon modes.     

Quantum interferometry via a coherent state mixed with a squeezed number state

We theoretically investigate the phase sensitivity with parity measurement on a Mach–Zehnder interferometer with a coherent state combined with a squeezed number state. Within a constraint on the total mean photon number, we find, via parity measurement, that the mixing of a coherent state and squeezed number state can give better phase sensitivity than mixing a coherent state and squeezed vacuum state when the phase shift deviates from the optimal phase φ= 0. In addition,we show that the classical Fisher information for parity measurement saturates the quantum Fisher information when the phase shift approaches to zero. Thus, the quantum Crame′r–Rao bound can be reached via the parity measurement in the case of φ= 0.     

Quantum state transfer between light and matter via teleportation

Quantum teleportation is an interesting feature of quantum mechanics. Entanglement is used as a link between two remote locations to transfer a quantum state without physically sending it – a process that cannot be realized utilizing merely classical tools. Furthermore it has become evident that teleportation is also an important element of future quantum networks and it can be an ingredient for quantum computation. This article reports for the first time the teleportation from light to atoms. In the experiment discussed, the quantum state of a light beam is transferred to an atomic ensemble. The key element of light‐atom entanglement created via a dispersive interaction lays the foundation for the protocol.     

Quantum state restoration and single-copy tomography for ground states of Hamiltonians

Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.     

Quantum teleportation of arbitrary two-qubit state via entangled cavity fields

We propose a new protocol for quantum teleportation of an arbitrary two qubit state via continuous variables entangling channel. In our scheme two pairs of entangled light fields are employed. An outstanding characteristic of this scheme is that arbitrary state of two atoms is transmitted deterministically and directly to another pair of atoms without the help of the other atoms.     

High quality and fast compressed sensing MRI reconstruction via edge-enhanced dual discriminator generative adversarial network

Generative adversarial networks (GAN) are widely used for fast compressed sensing magnetic resonance imaging (CSMRI) reconstruction. However, most existing methods are difficult to make an effective trade-off between abstract global high-level features and edge features. It easily causes problems, such as significant remaining aliasing artifacts and clearly over-smoothed reconstruction details. To tackle these issues, we propose a novel edge-enhanced dual discriminator generative adversarial network architecture called EDDGAN for CSMRI reconstruction with high quality. In this model, we extract effective edge features by fusing edge information from different depths. Then, leveraging the relationship between abstract global high-level features and edge features, a three-player game is introduced to control the hallucination of details and stabilize the training process. The resulting EDDGAN can offer more focus on edge restoration and de-aliasing. Extensive experimental results demonstrate that our method consistently outperforms state-of-the-art methods and obtains reconstructed images with rich edge details. In addition, our method also shows remarkable generalization, and its time consumption for each 256 × 256 image reconstruction is approximately 8.39 ms.