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In physics, quantum noise refers to the uncertainty of a physical quantity, due to its quantum origin. In certain situations, quantum noise appears as shot noise; for example, most optical communications use amplitude modulation, and thus, the quantum noise appears as shot noise only. For the case of uncertainty in the electric field in some lasers, the quantum noise is not just shot noise; uncertainties of both amplitude and phase contribute to the quantum noise. This issue becomes important in the case of noise of a quantum amplifier, which preserves the phase. The phase noise becomes important when the energy of the frequency modulation or phase modulation of waves is comparable to the energy of the signal (which is believed to be more robust with respect to additive noise than an amplitude modulation).
Origin of quantum noise
Quantum noise may appear in any system where conventional sources of noise (industrial noise, vibrations, fluctuations of voltage in the electric power supply, thermal noise due to Brownian motion, etc.) are somehow suppressed. Generally, quantum noise can be considered as the error of the description of any physical system within classical (not quantum) theory. In an electric circuit, the random fluctuations of a signal due to the discrete character of electrons can be called quantum noise. The random error of interferometric measurements of position, due to the discrete character of photons registered during measurement, can be attributed to quantum noise. Even the uncertainty of position of a probe in probe microscopy may lead to quantum noise, although this is not the dominant mechanism that determines the resolution of such a device. In most cases, quantum noise refers to the fluctuations of signal in extremely accurate optical systems with stabilized lasers and efficient detectors.
Coherent states and noise of a quantum amplifier
Although coherent states can be realized in wide variety of physical systems, they are primarily used to describe the state of laser light. Although the light from a laser can be interpreted as a classical wave, the generation of that light requires the language of quantum mechanics, and specificially, the use of coherent states to describe the system. For a total amount of photons of order of 108, which corresponds to a very moderate energy, the relative error of measurement of the intensity due the quantum noise is only of order of 10−5; this is considered to be of good precision for most of applications.
Quantum noise becomes important when considering the amplification of a small signal. Roughly, the quantum uncertainty of the quadrature components of the field is amplified as well as the signal; the resulting uncertainty appears as noise. This determines the lower limit of noise of a quantum amplifier.
A quantum amplifier is an amplifier which operates close to the quantum limit of its performance. The minimal noise of a quantum amplifier depends on the property of the input signal, which is reproduced at the output. In a narrow sense, the optical quantum amplifier reproduces both amplitude and phase of the input wave. Usually, the amplifier amplifies many modes of the optical field; special efforts are required to reduce the number of these modes. In the idealized case, one may consider just one mode of the electromagnetic field, which corresponds to a pulse with definite polarization, definite transversal structure and definite arrival time, duration and frequency, with uncertainties limited by the Heisenberg uncertainty principle. The input mode may carry some information in its amplitude and phase; the output signal carries the same phase but larger amplitude, roughly proportional to the amplitude of the input pulse. Such an amplifier is called phase-invariant amplifier.
Mathematically, quantum amplification can be represented with an unitary operator, which entangles the state of the optical field with internal degrees of freedom of the amplifier. This entanglement appears as quantum noise; the uncertainty of the field at the output is larger than that of the coherent state with the same amplitude and phase. The lower bound for this noise follows from the fundamental properties of the creation and annihilation operators.
- C. W. Gardiner and Peter Zoller, Quantum Noise, Springer-Verlag (1991, 2000, 2004)
- D. Kouznetsov; D. Rohrlich, R.Ortega (1995). "Quantum limit of noise of a phase-invariant amplifier". Physical Review A 52 (2): 1665–1569. arXiv:cond-mat/9407011. Bibcode:1995PhRvA..52.1665K. doi:10.1103/PhysRevA.52.1665.