Maximum Fidelity Research Articles

Fidelity of Gaussian Channels

A noisy Gaussian channel is defined as a channel in which an input field mode is subjected to random Gaussian displacements in phase space. We introduce the quantum fidelity of a Gaussian channel for pure and mixed input states, and we derive a universal scaling law of the fidelity for pure initial states. We also find the maximum fidelity of a Gaussian channel over all input states. Quantum cloning and continuous-variable teleportation are presented as physical examples of Gaussian channels to which the fidelity results can be applied.

Optimal probabilistic cloning and purification of quantum states

We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explictly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.

Decoherence of Nuclear Spin Quantum Memory in a Quantum Dot

Recently an ensemble of nuclear spins in a quantum dot have been proposed as a long-lived quantum memory. A quantum state of an electron spin in the dot can be faithfully transfered into nuclear spins through controlled hyperfine coupling. Here we study the decoherence of this memory due to nuclear spin dipolar coupling and inhomogeneous hyperfine interaction during the {\it storage} period. We calculated the maximum fidelity of writing, storing and reading operations. Our results show that nuclear spin dynamics can severely limits the performance of the proposed device for quantum information processing and storage based on nuclear spins.

Singularity of Farhi–Gutmann Analog Quantum Search**The project supported by National Natural Science Foundation of China under Grant No. 10131040

We show that the Farhi–Gutmann analog quantum search is a singular algorithm in the following sense: when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies, the maximum fidelity (transition probability) between the searching state and the target state is strictly less than 1 over the entire evolution period, and the first time to achieve this maximum fidelity is of order , whose behavior depends crucially on whether or not (here N is the total number of items, and the original Farhi–Gutmann case corresponds to ). Moreover, when and N tends to infinity, the maximum fidelity tends to zero, and the first time to achieve the maximum fidelity tends to a positive constant! The condition for guaranteeing the algorithm's efficiency is determined explicitly.

Maximum fidelity for a mirror symmetric set of qubit states

In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement, when the original quantum state is known to be a member of some specified set. This process provides both classical information about the state and a reproduction of that state. A suitable figure of merit for this process is the fidelity, which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state. We consider the maximization of the fidelity for a mirror symmetric set of three pure qubit states, but find that our results are more generally applicable. In contrast to previous examples, we find that the strategy which minimizes the probability of erroneously identifying the state does not generally maximize the fidelity.

Optimal teleportation with a mixed state of two qubits.

We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.

Programmable quantum measurement device that approximates all projective measurements on a qubit

AbstractA “universal” quantum measurement device is proposed. It can approximate any projective measurement on a qubit. The measurement basis is selected by the quantum state of a “program register''. The device is optimized with respect to maximal average fidelity. A contra‐intuitive result is that if two qubits in the same state are used as a program the average fidelity is higher than if the second program qubit is in the respective orthogonal state.

A pitfall in clinical photography: the appearance of skin lesions depends upon the illumination device.

Pictures of skin lesions are usually recorded with a camera equipped with a ring-type electric flash. In some cases the photographs do not reproduce the image perceived by the naked eye. To investigate the quality of photographs taken with the ring-type electric flash. Photographs of skin lesions and an experimental skin model were taken under different illumination conditions including a standard light source, full-spectrum fluorescent ceiling lights and the ring-type electric flash. Images taken under illumination with a standard light source box resembled those perceived by the naked eye. The full-spectrum fluorescent ceiling lights produced adequate results. Pictures taken with the ring-type electric flash showed some deficiencies including reduction in contrast, loss of shading and excess reflection. The ring-type electric flash is not an ideal device for recording skin lesions. An illumination device compatible with a standard light source should be employed to yield maximum fidelity.

Universal Measurement Apparatus Controlled by Quantum Software

We propose a quantum device that can approximate any projective measurement on a qubit-a quantum "multimeter." The desired measurement basis is selected by the quantum state of a "program register." Two different kinds of programs are considered and in both cases the device is optimized with respect to maximal average fidelity (assuming uniform distribution of measurement bases). Quantum multimeters exhibiting the covariance property are introduced and an optimal covariant multimeter with a single-qubit program register is found. Possible experimental realization of the simplest proposed device is presented.

Conclusive teleportation and entanglement concentration

Teleportation of a d-dimensional quantum state via a pure but partially entangled channel is studied. Two schemes are presented for conclusive teleportation aiming at both obtaining a faithful replica with optimal probability and achieving a maximum average fidelity of teleportation when conclusive teleportation fails. A single pair entanglement concentration scheme is also constructed.

Extremal equation for optimal completely positive maps

We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained by the optimal approximate transformation. The developed formalism is applied to universal-NOT gate, quantum cloning machines, quantum entanglers, and qubit theta-shifter.

Multiresolution analysis in fMRI: sensitivity and specificity in the detection of brain activation.

Multiresolution analysis of fMRI studies using wavelets is a new approach, previously reported to yield higher sensitivity in the detection of activation areas. No data are available, however, in the literature on the analytic approach and wavelet bases that produce optimum results. The present study was undertaken to assess the performance of different wavelet decomposition schemes by making use of a "gold standard," a realistic computer-simulated phantom. As activation areas are then known "a priori," accurate assessments of sensitivity, specificity, ROC curve area and spatial resolution can be obtained. This approach has allowed us to study the effect of different factors: the size of the activation area, activity level, signal-to-noise ratio (SNR), use of pre-smoothing, wavelet base function and order and resolution level depth. Activations were detected by performing t-tests in the wavelet domain and constructing the final image from those coefficients that passed the significance test at a given P-value threshold. In contrast to previously reported data, our simulation study shows that lower wavelet orders and resolution depths should be used to obtain optimum results (in terms of ROC curve area). The Gabor decomposition offers the maximum fidelity in preserving activation area shapes. No major differences were found between other wavelet bases functions. Data pre-smoothing increases ROC area for all but very small activation region sizes.

Optimal encoding and decoding of a spin direction

For a system of N spins 1/2 there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeroes of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in 1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.

A semidefinite program for distillable entanglement

We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and maximally correlated states. We conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1-local distillation.

Optimal quantum teleportation with an arbitrary pure state

We derive the maximum fidelity attainable for teleportation using a shared pair of d-level systems in an arbitrary pure state. This derivation provides a complete set of necessary and sufficient conditions for optimal teleportation protocols. We also discuss the information on the teleported particle which is revealed in course of the protocol using a non-maximally entangled state.

Optimal minimal measurements of mixed states

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean-average fidelity. We do this for up to three copies of the unknown state in a way that leads to the generalization to any number of copies, which we then present and prove.

Strategies and networks for state-dependent quantum cloning

State-dependent cloning machines that have so far been considered either deterministically copy a set of states approximately, or probablistically copy them exactly. In considering the case of two equiprobable pure states, we derive the maximum global fidelity of $N$ approximate clones given $M$ initial exact copies, where $N>M$. We also consider strategies which interpolate between approximate and exact cloning. A tight inequality is obtained which expresses a trade-off between the global fidelity and success probability. This inequality is found to tend, in the limit as $N{\to}{\infty}$, to a known inequality which expresses the trade-off between error and inconclusive result probabilities for state-discrimination measurements. Quantum-computational networks are also constructed for the kinds of cloning machine we describe. For this purpose, we introduce two gates: the distinguishability transfer and state separation gates. Their key properties are described

Optimal universal and state-dependent quantum cloning

We establish the best possible approximation to a perfect quantum cloning machine which produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a novel teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two non-orthogonal states, discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive a new upper bound on the quantum capacity of the depolarizing quantum channel.

The Use of Surface Electromyography in Biomechanics

This lecture explores the various uses of surface electromyography in the field of biomechanics. Three groups of applications are considered: those involving the activation timing of muscles, the force/EMG signal relationship, and the use of the EMG signal as a fatigue index. Technical considerations for recording the EMG signal with maximal fidelity are reviewed, and a compendium of all known factors that affect the information contained in the EMG signal is presented. Questions are posed to guide the practitioner in the proper use of surface electromyography. Sixteen recommendations are made regarding the proper detection, analysis, and interpretation of the EMG signal and measured force. Sixteen outstanding problems that present the greatest challenges to the advancement of surface electromyography are put forward for consideration. Finally, a plea is made for arriving at an international agreement on procedures commonly used in electromyography and biomechanics.

Noise and neuronal populations conspire to encode simple waveforms reliably.

Sensory systems rely on populations of neurons to encode information transduced at the periphery into meaningful patterns of neuronal population activity. This transduction occurs in the presence of intrinsic neuronal noise. This is fortunate. The presence of noise allows more reliable encoding of the temporal structure present in the stimulus than would be possible in a noise-free environment. Simulations with a parallel model of signal processing at the auditory periphery have been used to explore the effects of noise and a neuronal population on the encoding of signal information. The results show that, for a given set of neuronal modeling parameters and stimulus amplitude, there is an optimal amount of noise for stimulus encoding with maximum fidelity.