Noisy Probe Research Articles

Quantum illumination with noisy probes: Conditional advantages of non-Gaussianity

Entangled states, like the two-mode squeezed vacuum state, are known to give quantum advantage in the illumination protocol, a method to detect a weakly reflecting target submerged in a thermal background. We use non-Gaussian photon-added and -subtracted states, affected by local Gaussian noise on top of the omnipresent thermal noise, as probes in the illumination protocol. Based on the difference between the Chernoff bounds obtained with the coherent state and the non-Gaussian state having equal signal strengths, whose positive values denote quantum advantage in illumination, we highlight the hierarchy among non-Gaussian states, which is compatible with correlations per unit signal strength, although the Gaussian states offer the best performance. Interestingly, such hierarchy is different when comparisons are made using the Chernoff bounds. The entire analysis is performed in the presence of different imperfect apparatus like faulty twin-beam generator, imperfect photon addition (subtraction) as well as with noisy non-Gaussian probe states.

Phase noise mitigation by a realistic optical parametric oscillator

We address the exploitation of an optical parametric oscillator (OPO) in the task of mitigating, at least partially, phase noise produced by phase diffusion. In particular, we analyze two scenarios where phase diffusion is typically present. The first one is the measurement of the phase of a noisy optical field, while the second involves a quantum estimation scheme of a phase shift imposed on a noisy probe. In both cases, we prove that an OPO may lead to a partial or full compensation of the noise.

Robust Quantum Metrology With Explicit Symmetric States

Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to be noisy, and we have to make do with noisy probe states. We prove that, for a set of carefully chosen symmetric probe states that lie within certain quantum error correction codes, quantum metrology exhibits an advantage over classical metrology even after the probe states are corrupted by a constant number of erasure and dephasing errors. These probe states prove useful for robust metrology not only in the NISQ regime, but also in the asymptotic setting where they achieve Heisenberg scaling. This brings us closer towards making robust quantum metrology a technological reality.

The capacity of the dense associative memory networks

This paper revisits the dense associative memory (DAM) networks and studies rigorously the capacity of the DAM networks. We present the capacity theorem of the DAM networks with an attraction radius or a noise level from the messages and prove that the probe can converge to the targeted message just after the one-step update. Under this convergence, the capacity of DAM networks is between a lower bound and an upper bound. Although when the attraction radius is 0.0 away from the messages, i.e. noiseless, previous literature provides an approximate result. However, a rigorous proof is not given in this study. In addition, we consider a more general notion of capacity which allows the retrieval of messages from noisy probes (the attraction radius is not 0.0). We demonstrates that the convergence result can be acquired just after the one-step update when the probe is a corrupted version with a Gaussian noise from one message. We further provide simulated experiments to validate theorems herein.

A robust face super-resolution algorithm and its application in low-resolution face recognition system

In real-world surveillance scenario, the face recognition (FR) systems pose a lot of challenges due to the captured low-resolution (LR) and noisy probe images. A new face super-resolution (SR) algorithm is proposed to design a recognition model overcoming the challenges of existing FR systems. The proposed SR algorithm inherits the merits of functional-interpolation and dictionary-based SR techniques. The functional interpolation assists in generating more discriminable output, whereas the dictionary-based approach assists in eliminating noise effects from the reconstruction process. Consequently, it produces more discriminable and noise-free high-resolution (HR) images from captured noisy LR probe images, suitable for real-world problems like low-resolution face recognition. The results obtained from the experiments performed on several popular face image datasets including FEI, FERET, and CAS-PEAL-R1 show that the proposed algorithm performs better than all the comparative SR methods.

Application of a Langmuir probe AC technique for reliable access to the low energy range of electron energy distribution functions in low pressure plasmas

The electron energy distribution function (EEDF) in low pressure plasmas is typically evaluated by using the second derivative d2I/dV2 of a Langmuir probe I–V characteristic (Druyvesteyn formula). Since measured probe characteristics are inherently noisy, two-time numerical differentiation requires data smoothing techniques. This leads to a dependence on the employed filtering technique, and information particularly in the region near the plasma potential can easily get lost. As an alternative to numerical differentiation of noisy probe data, a well-known AC probe technique is adopted to measure d2I/dV2 directly. This is done by superimposing a sinusoidal AC voltage of 13 kHz on the probe DC bias and performing a Fourier analysis of the current response. Parameters such as the modulation amplitude (up to 1.5 V) and the number of applied sine oscillations per voltage step of the DC ramp are carefully chosen by systematic parameter variations. The AC system is successfully benchmarked in argon and applied to hydrogen plasmas at a laboratory inductively coupled plasma experiment (4–10 Pa gas pressure, 300–1000 W RF power). It is shown that the EEDF is reliably accessible with high accuracy and stability in the low energy range. Hence, a trustworthy determination of basic plasma parameters by integration of the EEDF can be provided.

Improving Quantum Metrology via Purifying and Distilling Noisy Probe States

AbstractIn quantum metrology, the precision of unknown parameter estimation is studied in the quantum regime, and the choice of the probe state plays an important role in determining the precision of the parameter to be estimated. The quality of quantum metrology will be reduced in the presence of quantum noise during the memory time of probe states after preparation. Meanwhile the noisy probe state can be manipulated by different protocols such as single‐qubit purification, entanglement purification, and entanglement distillation etc. In this paper, the effects of these manipulations on the usefulness, that is, quantum Fisher information (QFI), of the noisy probe state in quantum metrology are studied. The results show that joint operations in single‐qubit purification and entanglement purification processes play positive roles in enhancing the QFI of the probe states, and local measurements in entanglement purification and entanglement distillation processes play both positive and negative roles in enhancing the QFI of the probe states. In this sense, single‐qubit purification will always be helpful in parameter estimation by using single qubits as probe, and entanglement purification process maybe more suitable for improving the estimation precision when entangled‐state probe is adopted.

Noisy frequency estimation with noisy probes

We consider frequency estimation in a noisy environment with noisy probes. This builds on previous studies, most of which assume that the initial probe state is pure, while the encoding process is noisy, or that the initial probe state is mixed, while the encoding process is noiseless. Our work is more representative of reality, where noise is unavoidable in both the initial state of the probe and the estimation process itself. We prepare the probe in a GHZ diagonal state, starting from n + 1 qubits in an arbitrary uncorrelated mixed state, and subject it to parameter encoding under dephasing noise. For this scheme, we derive a simple formula for the (quantum and classical) Fisher information, and show that quantum enhancements do not depend on the initial mixedness of the qubits. That is, we show that the so-called ‘Zeno’ scaling is attainable when the noise present in the encoding process is time inhomogeneous. This scaling does not depend on the mixedness of the initial probe state, and it is retained even for highly mixed states that can never be entangled. We then show that the sensitivity of the probe in our protocol is invariant under permutations of qubits, and monotonic in purity of the initial state of the probe. Finally, we discuss two limiting cases, where purity is either distributed evenly among the probes or concentrated in a single probe.

Probabilistic Analysis of Probe Reliability in Differential Gene Expression Studies with Short Oligonucleotide Arrays

Probe defects are a major source of noise in gene expression studies. While existing approaches detect noisy probes based on external information such as genomic alignments, we introduce and validate a targeted probabilistic method for analyzing probe reliability directly from expression data and independently of the noise source. This provides insights into the various sources of probe-level noise and gives tools to guide probe design.

Squeezing restoration by a noisy probe from a classically correlated environment

Quantum squeezing, an irreducible resource for quantum communication and quantum metrology, is very fragile and can be lost due to classical noise produced by an environment. We show that a classical correlation between the squeezed signal and the classical probe partially monitoring noise from the environment can be used as a resource to restore the lost squeezing. Two basic methods, the feed-forward restoration and the unitary decoupling, are proposed to exploit this classical correlation. They are mutually compared for high and low squeezing and also in the different regimes of correlated classical noise. On one side, a robustness against classical probe noise to restore at least nonzero squeezing is discussed, and on the other side, a complete revealing of the high squeezing by a squeezed probe and unitary decoupling is proposed.

Designs of Second-Order Associated Memory Networks with Threshold Logics: Winner-Take-All and Selective Voting

The capacity of an order-d associative memory model is O(N d /logN) where N is the memory size in bit. In contrast, the capacity of the Hopfield network is limited to O(N/logN). Among higher order associative memory models (d > 1), the second order memory (d = 2) has attractive properties: a relatively small implementation cost of O(N 2 ), a small number of spurious states, and the presence of a diagonalization form. Due to these properties, it is of both practical and scientific interests to investigate efficient computational mechanisms of such network. One disadvantage of higher order associative memory is that it cannot be implemented with simple threshold neurons or McCulloch-Pitts neurons, thus a direct implementation of its computational mechanism on a biological substrate is questionable and its silicon implementation is expensive. In this paper, we propose two approximation models of a second order associative memory using threshold logics. Both are two-layered and employ eigenvalue decomposition of the correlation tensor. The first model uses a winner-takeall mechanism and the second uses a weighted voting by those with significant responses. Architectural-level designs of these memory models are presented. Extensive numerical simulations demonstrate effectiveness of the proposed models in retrieving contents with noisy probe vectors.

A test for the consecutive ones property on noisy data--application to physical mapping and sequence assembly.

A (0,1)-matrix satisfies the consecutive ones property (COP) for the rows if there exists a column permutation such that the ones in each row of the resultant matrix are consecutive. The consecutive ones test is useful for physical mapping and DNA sequence assembly, for example, in the STS content mapping of YAC library, and in the Bactig assembly based on STS as well as EST markers. The linear time algorithm by Booth and Lueker (1976) for this problem has a serious drawback: the data must be error free. However, laboratory work is never flawless. We devised a new iterative clustering algorithm for this problem, which has the following advantages: 1. If the original matrix satisfies the COP, then the algorithm will produce a column ordering realizing it without any fill-in. 2. Under moderate assumptions, the algorithm can accommodate the following four types of errors: false negatives, false positives, nonunique probes, and chimeric clones. Note that in some cases (low quality EST marker identification), NPs occur because of repeat sequences. 3. In case some local data is too noisy, our algorithm could likely discover that and suggest additional lab work to reduce the degree of ambiguity in that part. 4. A unique feature of our algorithm is that, rather than forcing all probes to be included and ordered in the final arrangement, our algorithm would delete some noisy probes. Thus, it could produce more than one contig. The gaps are created mostly by noisy probes.

Skill-based interpretation of noisy probe signals enhanced with a genetic algorithm

The paper presents the design and evaluation of an adaptive signal processing procedure based on human skill. The focus is on interpreting probe signals detected in gas–liquid flow in the presence of noise where existing signal interpretation techniques may encounter difficulties. Interpretation of a probe signal requires construction of a corresponding two-state signal that denotes the presence of the phases, i.e. gas and liquid, at the probe tip. To develop a computer procedure that would imitate a skilled operator in probe signal interpretation, manual knowledge acquisition and evolutionary optimization were employed. First, a prototype signal interpretation procedure based on operator skill was designed, and the procedure parameters were then optimized with a genetic algorithm. In the optimization process, a two-state signal reconstructed from the probe signal by an operator was used as a reference. The robustness of the approach was tested in a series of numerical experiments. They included local evaluation on training and test signals, calculation of global void fraction values, and an assessment of variability among different experts. The results showed that the developed technique is highly consistent with the operator way of signal interpretation and represents a reliable prerequisite for gas–liquid flow measurements.

Coherence and intensity statistics in phase-conjugate resonators

The spectra, coherence properties, and intensity fluctuations of waves generated by reflections of a noisy probe field from a phase-conjugate Fabry-Perot resonator are discussed. The emphasis of the analysis is on the spectral response of the resonator. The results obtained are in fill agreement with those derived using specific noise models in the time domain. Advantages of the frequency-domain analyses include full tractability of general probe-wave noise models and fast convergence of numerical computations. The reflected-wave coherence properties reveal an interesting periodic structure due to multiple intracavity reflections. The intensity fluctuation levels, which depend on the statistical models, are calculated explicitly for pure Markovian phase noise and Gaussian amplitude noise of the probe. Combinations of these two, yielding simple laser models, and other extensions of noise effects in phase-conjugate resonators are briefly discussed. >

Algorithmic Trimming on Active Circuitry

The active circuitry for a digital autoranging multimeter has been fabricated on a single hybrie substrate measuring 2.8 X 3.8 cm. The hybrid is realized using tantalum nitride thin film technology. A high temperature passivation process stabilizes the tantalum nitride film. During this process, the absolute value of resistance changes substantially. This change makes the technology unusable in some precision applications. In order to overcome this problem and take advantage of the film's inherently excellent stability, laser trimming is utilized to adjust the absolute value. The result is a stable precision resistor. When the end result of the laser trimming process is a resistor of predetermined value, the operation can be performed by "passive trimming." In many cases, it is desirable to trim the resistor to an unknown value in order to obtain a given circuit response. When this is done to an operating circuit, the procedure is known as "active trimming." In general, a relationship can be determined between a known stimulus and its desired circuit response. The trim procedure can be designed to cause this desired relat onship. Specific algorithms and techniques have been developed to test the sensitivity of a circuit parameter to a given change in trim resistance. The computer controlled system uses this information to determine the succeeding trim magnitude. The use of a computer controller allows the system to handle complicated nonlinear stimulus-response data. Once a hybrid is trimmed, it is effectively a finished product. Since it has been calibrated during the trimming process, there is no need for manual adjustment. One difficulty associated with active laser trimming is duplicating the external circuit while at the same instant connecting the hybrid substrate to noisy probe rings, loading it with capacitances, and subjecting it to-the hostile environment of electromechanical controls. This paper will deal primarily with algorithms developed for active trim and the problems of electrically interfacing the system with the hybrid under test. Most of this experience was achieved during the development of the Hewlett-Packard Model 970A Probe Multimeter.