Selective and efficient quantum process tomography without ancilla

Several methods, known as quantum process tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we present a new method for quantum process tomography. We describe a new algorithm that can be used to selectively estimate any parameter characterizing a quantum process. Unlike any of its predecessors this new quantum tomographer combines two virtues: it requires investing a number of physical resources scaling polynomially with the number of qubits and at the same time it does not require any ancillary resources. We present the results of the first implementation of this quantum device, characterizing quantum processes affecting two qubits encoded in heralded single photons. Even for this small system our method displays clear advantages over the other existing ones.     

Ancilla-assisted quantum process tomography

Complete and precise characterization of a quantum dynamical process can be achieved via the method of quantum process tomography. Using a source of correlated photons, we have implemented several methods, each investigating a wide range of processes, e.g., unitary, decohering, and polarizing. One of these methods, ancilla-assisted process tomography (AAPT), makes use of an additional "ancilla system," and we have theoretically determined the conditions when AAPT is possible. Surprisingly, entanglement is not required. We present data obtained using both separable and entangled input states. The use of entanglement yields superior results, however.     

Accuracy characteristics for quantum process tomography using superconductor phase qubits

A method for the precision statistical control of quantum processes is developed on the basis of applications of superconductor phase qubits. A detailed analysis of tomographic accuracy for a 2-qubit SQiSW gate arising due to capacitive coupling between qubits is performed by means of universal quantum tomography. The presented approach can be used to solve problems of quality and efficiency in superconductor quantum information technologies.     

基于核磁共振的子空间量子过程重构

基于三核自旋量子系统实现了内嵌两量子位子空间量子过程重构.通过输入完备态集合对执行的量子过程进行了表征.由于量子过程内嵌于子空间,使得重构实验所需输入次数及时间显著减少,同时实验尽量避免使用时间较长的J偶合演化,有效控制了系统的退相干。     

A more informative estimation procedure for the parameters of a diffusion process

The estimation procedures for the parameters of a diffusion process with constant coefficients have mainly focused on volatility. Nevertheless, even if the knowledge of the volatility alone suffices to compute the Black and Scholes option prices, other financial application models assume that the price dynamics follows a log-normal process and requires the knowledge of both parameters. On the other hand, while the usual ML estimator of volatility gives satisfactory results, the estimation of drift is much less accurate; moreover, the drift-estimated value highly depends on the phases of the business cycle included in the sample data. This contribution explicitly imposes a risk aversion or risk neutral assumption into the ML estimation procedure and makes a constrained maximization of the sample likelihood function. The aim is twofold: to obtain estimated values which are consistent with a widely accepted assumption and use the risk aversion constraint in order to improve the accuracy of the estimates.     

Linear optical implementation of a quantum network for quantum estimation

We present an interferometer for simulating the quantum network for quantum estimation proposed by A.K. Ekert et al. [A.K. Ekert, C.M. Alves, D.K.L. Oi, M. Horodecki, P. Horodecki, L.C. Kwek, Phys. Rev. Lett. 88 (2002) 217901]. We experimentally perform overlap measurements of two single-qubit states with linear optical elements. The scheme is generalized to perform estimation of Trρ³.     

Experimental investigation of a nonideal two-qubit quantum-state filter by quantum process tomography

We used quantum process tomography to investigate and identify the function of a nonideal two-qubit quantum-state filter subject to various degrees of decoherence. We present a simple decoherence model that explains the experimental results and point out that a beam splitter followed by a postselection process is not, as commonly believed, a singlet-state filter. In the ideal case it is a triplet-state filter.     

Generalized limits for single-parameter quantum estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with k-system parameter-sensitive terms, the quantum limit scales as 1/Nk, where N is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.     

Diagnosis, prescription, and prognosis of a bell-state filter by quantum process tomography

We apply the techniques of quantum process tomography to characterize errors and decoherence in a prototypical two-photon operation, a singlet-state filter. The quantum process tomography results indicate a large asymmetry in the process and also the required operation to correct for this asymmetry. We quantify residual errors and decoherence of the filtering operation after this modification.     

Reconstructing quantum states via quantum tomography and atom interferometry

Received: 25 July 1997     

Fast quantum algorithm for numerical gradient estimation

Given a black box for f, a smooth real scalar function of d real variables, one wants to estimate [symbol: see text]f at a given point with n bits of precision. On a classical computer this requires a minimum of d + 1 black box queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n.     

Optimal quantum circuits for general phase estimation

We address the problem of estimating the phase phi given N copies of the phase-rotation gate uphi. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi for phi depends only on the difference phi-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.     

Parallel state transfer and efficient quantum routing on quantum networks

We study the routing of quantum information in parallel on multidimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits. We show that perfect parallel state transfer is possible for certain networks of harmonic oscillator modes. We extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is optimal and robust in the presence of dissipation and finite bandwidth.     

Robustness of raw quantum tomography

We scrutinize the effects of non-ideal data acquisition on the tomograms of quantum states. The presence of a weight function, schematizing the effects of a finite window or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms.     

Maximally efficient protocols for direct secure quantum communication

Two protocols for deterministic secure quantum communication (DSQC) using GHZ-like states have been proposed. It is shown that one of these protocols is maximally efficient and that can be modified to an equivalent protocol of quantum secure direct communication (QSDC). Security and efficiency of the proposed protocols are analyzed and compared. It is shown that dense coding is sufficient but not essential for DSQC and QSDC protocols. Maximally efficient QSDC protocols are shown to be more efficient than their DSQC counterparts. This additional efficiency arises at the cost of message transmission rate.     

Optical Fresnel transformation and quantum tomography

Corresponding to optical Fresnel transformation characteristic of a ray transfer matrix (A,B,C,D),AD-BC=1, there exists Fresnel operator F(A,B,C,D) in quantum optics, we show that under the Fresnel transformation the pure-state position density ∣x〉〈x∣ becomes density operator ∣x〉_s,rs,r〈x∣, which is just the Radon transform of the Wigner operator, i.e.,

     

Review: Characterizing and quantifying quantum chaos with quantum tomography

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in information gain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory in the fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different classes of maps and show that these bounds are realized by fully chaotic quantum systems.     

Invariant information and quantum state estimation

The invariant information, introduced by C. Brukner and A. Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)], is reconsidered from the point of view of quantum state estimation. We show that this quantity is directly related to the mean error of the standard reconstruction from the measurement of a complete set of mutually complementary observables. We give its generalization in terms of the Fisher information. Provided that the optimum reconstruction is adopted, the information loses its invariant character.     

Optimization of a quantum tomography protocol for polarization qubits

An operational method has been proposed for estimating the efficiency of quantum cryptography protocols for quantum states with discrete variables. The method is based on the estimate of the quality of the protocol by means of a universal asymptotic distribution of the characteristic of the accuracy of the reconstruction of the quantum state, which is called fidelity. For a specially designed measurement matrix, the condition number, which is minimal for the optimal protocol, is introduced. The method has been tested in a numerical simulation and real experiments with polarization qubits. It has been shown that the optimal choice of a polarization transformer makes it possible to strongly improve the quality of the reconstruction of states.