Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the Quantum Correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our work demonstrates the quantum/classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.
In this work, the global white-noise model is proved from first principles. The adherence of NISQ hardware to the global white-noise model is used to perform noise mitigation using Classical White-noise Extrapolation (CLAWE).
Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudo-noise) as performed in Spread-Spectrum communication used presently in Wi-Fi and Smartphone Telecommunication systems. Quantum communication based on entanglement is another route for securing communications as demonstrated by several important experiments described in this work. The central role played by the photon in unifying the description of Classical and Quantum noise as major ingredients of secure communication systems is highlighted and described on the bas…
Quantum fluctuations yield inevitable noises in quantum detection. We derive an upper bound of signal to noise ratio for arbitrary quantum detection described by trace-class operators with discrete spectra. The bound is independent of observables to be detected and is computed by quantum fidelity of two initial quantum states. We provide applications of the upper bound.
We demonstrate a die-level balanced homodyne receiver for coherent optical access and continuous-variable quantum applications, featuring a 40dB CMRR up to 1GHz and a high quantum-to-classical noise ratio of 26.8dB at 12.3mW of LO power. 500Mb/s QPSK transmission was accomplished with a sensitivity of -55.8dBm.
Recently, the Gaussian optimizer conjecture in quantum information theory was confirmed for bosonic Gaussian gauge-covariant or contravariant channels. These results use the i.i.d. model of the quantum noise. In this paper we consider quantum Gaussian signal+noise model with time-continuous stationary coloured noise. A proof of the coding theorem for the classical capacity of quantum broadband gauge-covariant Gaussian channels is given. We also discuss and compare the "broadband" and the "bandpass" models of time-continuous time-continuous stationary coloured noise.
We demonstrate a sub-shot-noise-limit discrimination of on-off keyed coherent signals by an optimal displacement quantum receiver in which a superconducting transition edge sensor is installed. Use of a transition edge sensor and a fiber beam splitter realizes high total detection efficiency and high interference visibility of the receiver and the observed average error surpasses the shot-noise-limit in a wider range of the signal power. Our technique opens up a new technology for the sub-shot-noise-limit detection of coherent signals in optical communication channels.
We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are…
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical noises are both present, their combined effect on a system's dynamics is not necessarily a simple sum of the two individual effects. Thus previous master equations for open systems and those for classical noise, even when jointly used, may not capture the full physics. Our formalism can determine whether there is interference between quantum and classical n…
The Hanbury Brown Twiss (HBT) interferometer was proposed to observe intensity correlations of starlight to measure a star's angular diameter. As the intensity of light that reaches the detector from a star is very weak, one cannot usually get a workable signal-to-noise ratio. We propose an improved HBT interferometric scheme introducing optical parametric amplifiers into the system, to amplify the correlation signal, which is used to calculate the angular diameter. With the use of optical parametric amplifiers, the signal-to-noise ratio can be increased up to 400 percent.
The signal-to-noise ratio for heterodyne laser radar with a coherent target-return beam and a squeezed local-oscillator beam is lower than that obtained using a coherent local oscillator, regardless of the method employed to combine the beams at the detector.
Twin-Signal-Recycling (TSR) builds on the resonance doublet of two optically coupled cavities and efficiently enhances the sensitivity of an interferometer at a dedicated signal frequency. We report on the first experimental realization of a Twin-Signal-Recycling Michelson interferometer and also its broadband enhancement by squeezed light injection. The complete setup was stably locked and a broadband quantum noise reduction of the interferometers shot noise by a factor of up to 4\,dB was demonstrated. The system was characterized by measuring its quantum noise spectra for several tunings of …
As part of the effort to make use of squeezed states of light for detection of sub-shot-noise optical signals, we study the balanced heterodyne scheme, for which the corresponding spectral density of the photocurrent fluctuations produced at the output of the detector is calculated as the Fourier transform of their autocorrelation function. Our analysis shows that, for maximal signal-to-noise ratio enhancement by use of squeezed states of light, an optical signal to be measured must be carried in the squeezed quadrature of the carrier field. We discuss how "the additional heterodyne noise" can…
We present a simple model of quantum communication where a noisy quantum channel may benefit from the addition of further noise at the decoding stage. We demonstrate enhancement of the classical information capacity of an amplitude damping channel, with a predetermined detection threshold, by the addition of noise in the decoding measurement.
The amplification obtained using weak values is quantified through a detailed investigation of the signal to noise ratio for an optical beam deflection measurement. We show that for a given deflection, input power and beam radius, the use of interferometric weak values allows one to obtain the optimum signal to noise ratio using a coherent beam. This method has the advantage of reduced technical noise and allows for the use of detectors with a low saturation intensity. We report on an experiment which improves the signal to noise ratio for a beam deflection measurement by a factor of 54 when c…
Noise usually has an unwelcome influence on system performance. For instance, noise inevitably affects the low-frequency mechanical freedom in optomechanical experiments. However, we investigate here the beneficial effects of thermal noise on a basic optomechanical system with parametric instability. In a regime near parametric instability, it is found that thermal noise in the mechanical freedom can sustain long-term quasi-coherent oscillations when the system would otherwise remain in the equilibrium state. In an overlapping regime of parametric instability and bistability, intermittent swit…
We find a tight upper bound for the classical capacity of quantum thermal noise channels that is within $1/\ln 2$ bits of Holevo's lower bound. This lower bound is achievable using unentangled, classical signal states, namely displaced coherent states. Thus, we find that while quantum tricks might offer benefits, when it comes to classical communication they can only help a bit.
Quantum sensing, using quantum properties of sensors, can enhance resolution, precision, and sensitivity of imaging, spectroscopy, and detection. An intriguing question is: Can the quantum nature (quantumness) of sensors and targets be exploited to enable schemes that are not possible for classical probes or classical targets? Here we show that measurement of the quantum correlations of a quantum target indeed allows for sensing schemes that have no classical counterparts. As a concrete example, in case where the second-order classical correlation of a quantum target could be totally concealed…
Quantum decoherence arises due to uncontrollable entanglement between a system with its environment. However the effects of decoherence are often thought of and modeled through a simpler picture in which the role of the environment is to introduce classical noise in the system's degrees of freedom. Here we establish necessary conditions that the classical noise models need to satisfy to quantitatively model the decoherence. Specifically, for pure-dephasing processes we identify well-defined statistical properties for the noise that are determined by the quantum many-point time correlation func…
We calculate the two-qubit disentanglement due to classical random telegraph noise using the quasi-Hamiltonian method. This allows us to obtain analytical results even for strong coupling and mixed noise, important when the qubits have tunable working point. We determine when entanglement sudden death and revival occur as functions of qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, we show that the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation. A physical inte…
We demonstrate that a phase-insensitive parametric amplifier, coupled to a quantum correlated source, can be used as a quantum information tap for noiseless three-way signal splitting. We find that the output signals are amplified noiselessly in two of the three output ports while the other can more or less keep its original input size without adding noise. This scheme is able to cascade and scales up for efficient information distribution in an optical network. Furthermore, we find this scheme satisfies the criteria for a non-ideal quantum non-demolition (QND) measurement and thus can serve a…
We investigate the maximum signal to noise ratio per unit time that can be achieved for a spin 1/2 particle subjected to a periodic pulse sequence. Optimal control techniques are applied to design the control field and the position of the steady state, leading to the best signal to noise performance. A complete geometric description of the optimal control problem is given in the unbounded case. We show the optimality of the well-known Ernst angle solution, which is widely used in spectroscopic and medical imaging applications, over a large control space allowing use of shaped pulses.
Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be defined by the mutual information of the multipartite measurement outcomes. In general the quantum discord of an arbitrary quantum state involves an optimisation of over the classical measurements which is hard to compute. In this paper, we examine the quantum discord in the experimentally relevant case when the quantum states are Gaussian and the measuremen…
We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical results for few modes are presented. They confirm the possibility to enhance the classical information rate with the aid of entangled inputs, and show a likely asymptotic behavior that should lead to the full capacity of the channel.
Imagine that you have several sets of two coupled qubits, but you do not know the parameters of their Hamitonians. How to determine these without resorting to the usual spectroscopy approach to the problem? Based on numerical modeling, we show that all the parameters of a system of two coupled qubits can be determined by applying to it an external classical noise and analysing the Fourier spectrum of the elements of the system's density matrix. In particular, the interlevel spacings as well as the strength and sign of qubit-qubit coupling can be determined this way.
We analyze the properties of nonclassical number states, specifically squeezed number states D(a)S(z)|n >, and find their maximum signal-to-quantum noise ratio. It is shown that the optimal signal-to-quantum noise ratio for these states decreases as 1/(2n+1)2, where n is the photon number, from the optimal value as derived by Yuen.
We propose an interferometry technique, by using electromagnetically induced transparency phenomena, for measuring classical force. The classical force is estimated by measuring the phase at the output of the interferometer. The proposed measurement mechanism satisfies quantum non-demolition measurement conditions leading to back-action evasion. We further derive the sufficient condition under which the thermal noise in the interferometer is negligible. With no back-action noise and no thermal noise, the sensitivity of this technique is limited by shot noise only.
The advantages of weak measurements, and especially measurements of imaginary weak values, for precision enhancement, are discussed. A situation is considered in which the initial state of the measurement device varies randomly on each run, and is shown to be in fact beneficial when imaginary weak values are used. The result is supported by numerical calculation and also provides an explanation for the reduction of technical noise in some recent experimental results. A connection to quantum metrology formalism is made.
A Systematic Study of Noise Effects in Hybrid Quantum-Classical Machine Learning
SVKM's NMIMS Mukesh Patel School of Technology Management and Engineering（SVKM NMIMS 穆克什·帕特尔技术与工程学院）；Lahore University of Management Sciences（拉合尔管理科学大学）
In this paper we are interested to model quantum signal by statistical signal processing methods. The Gaussian distribution has been considered for the input quantum signal as Gaussian state have been proven to a type of important robust state and most of the important experiments of quantum information are done with Gaussian light. Along with that a joint noise model has been invoked, and followed by a received signal model has been formulated by using convolution of transmitted signal and joint quantum noise to realized theoretical achievable capacity of the single quantum link. In joint qua…
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small c…
We investigate the decay of two-qubit entanglement caused by the influence of classical noise. We consider the whole spectrum of cases ranging from independent to fully correlated noise affecting each qubit. We take into account different spatial symmetries of noises, and the regimes of noise autocorrelation time. The latter can be either much shorter than the characteristic qubit decoherence time (Markovian decoherence), or much longer (approaching the quasi-static bath limit). We express the entanglement of two-qubit states in terms of expectation values of spherical tensor operators which a…
We study the quantum to classical transition in Boson Sampling by analysing how $N$-boson interference is affected by inevitable noise in an experimental setup. We adopt the Gaussian noise model of Kalai and Kindler for Boson Sampling and show that it appears from some realistic experimental imperfections. We reveal a connection between noise in Boson Sampling and partial distinguishability of bosons, which allows us to prove efficient classical simulatability of noisy no-collision Boson Sampling with finite noise amplitude $ε$, i.e., $ε= Ω(1)$ as $N\to \infty$. On the other hand, using an equ…
Correlation plenoptic imaging (CPI) is a scanning-free diffraction-limited 3D optical imaging technique exploiting the peculiar properties of correlated light sources. CPI has been further extended to samples of interest to microscopy, such as fluorescent or scattering objects, in a modified architecture named correlation light-field microscopy (CLM). Interestingly, experiments have shown that the noise performances of CLM are significantly improved over the original CPI scheme, leading to better images and faster acquisition. In this work, we provide a theoretical foundation to such advantage…
We introduce the concepts of Poisson brackets for classical noise, and of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving the full (system and noise) Poisson structure is obtained. We show that, once the classical stochastic model is required to preserve the joint system and noise Poisson bracket, it has much in common with quantum markovian models.
The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with polynomial coefficients, - demodulations is achieved thanks to new algebraic estimation techniques. Operational calculus, differential algebra and nonstandard analysis are the main mathematical tools.
