Quantum noise is any noise arising from quantum mechanical phenomena such as field quantization or the uncertainty principle. Quantum noise differs from classical noise fundamentally not only in the kinds of phenomena from which it arises, but also in key characteristic features such as its spectral density and temperature dependence. For example, the uncertainty principle says that some groups of observables cannot simultaneously be known with arbitrary precision. As a result, measuring one observable to some precision can actually impose a limit on how precisely another observable can be known. Even for a system in its ground state -- at zero temperature -- this quantum indeterminacy can cause fluctuations in measured observable quantities. Such fluctuations are known as zero-point energy fluctuations. Quantum noise can also come from the discrete nature of the components of flowing currents approximated as continuous, such as electrons and photons. An example of this form of quantum noise is shot noise as coined by J. Verdeyen which comes from the discrete arrival of photons or electrons in a detector. Because these quanta arrive randomly in time, even a perfectly steady current or light beam exhibits fluctuations in the detected signal. In most systems, classical noise dominates over quantum noise. Under everyday environmental conditions, classical fluctuations are typically several orders of magnitude larger than quantum fluctuations, and thus mask their effect. Quantum noise generally only becomes visible after suppressing the effects of conventional noise sources such as thermal fluctuations, mechanical vibrations, and industrial noise by mechanically isolating a system, cooling it to a millikelvin range, and using extremely low-noise electronics for control and readout. This is why quantum noise is a major engineering problem in superconducting circuits and in the LIGO gravitational wave observatory, but not in many conventional settings. Even if all classical noise is eliminated, devices such as detectors and amplifiers will still be affected by quantum noise. As a result, experimental physicists define an "ideal" or "quantum-limited" amplifier or detector as one with only that noise which arises from quantum sources. The term "quantum noise" is sometimes used in the fields of quantum information and quantum computing as an umbrella term for unwanted environmental disturbances that affect quantum systems and cause decoherence. An isolated quantum system, such as a qubit, has a state that will evolve deterministically. But in an open system, such as those found in nature, the qubit interacts with uncontrolled degrees of freedom in its environment, introducing fluctuations which are commonly referred to as quantum noise. This is distinct from the above definition, which specifically concerns intrinsic noise due to the nature of quantum mechanics, not all environmental sources of noise and decoherence. In practice, however, definitions of quantum noise often include environmental or external disturbances affecting quantum systems.
History
Principles
Noise theory A signal's noise is quantified as the Fourier transform of its autocorrelation. The autocorrelation of a signal is given as
G v v ( t − t ′ ) = ⟨ V ( t ) V ( t ′ ) ⟩ , {\displaystyle G_{vv}(t-t')=\langle V(t)V(t')\rangle ,}
which measures when our signal is positively, negatively or not correlated at different times t {\displaystyle t} and t ′ {\displaystyle t'} . The time average, ⟨ V ( t ) ⟩ {\displaystyle \langle V(t)\rangle } , is zero and our V ( t ) {\displaystyle V(t)} is a voltage signal. Its Fourier transform is
V ( ω ) = 1 T ∫ 0 T V ( t ) e i ω t d t {\displaystyle V(\omega )={\frac {1}{\sqrt {T}}}\int _{0}^{T}V(t)e^{i\omega t}dt}
because we measure a voltage over a finite time window. The Wiener–Khinchin theorem generally states that a noise's power spectrum is given as the autocorrelation of a signal, i.e.,
S v v ( ω ) = ∫ − ∞ + ∞ e i ω t G v v d t = ∫ − ∞ + ∞ e i ω t ⟨ | V ( ω ) | 2 ⟩ d t {\displaystyle S_{vv}(\omega )=\int _{-\infty }^{+\infty }e^{i\omega t}G_{vv}dt=\int _{-\infty }^{+\infty }e^{i\omega t}\langle |V(\omega )|^{2}\rangle dt} The above relation is sometimes called the power spectrum or spectral density. In the above outline, we assumed that
Our noise is stationary or the probability does not change over time. Only the time difference matters. Noise is due to a very large number of fluctuating charge so that the central limit theorem applied, i.e., the noise is Gaussian or normally distributed.
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