On the detectabillity limit of coherent optical signals in thermal radiation

The problem of detecting a completely known coherent optical signal in a thermal background radiation is considered. The problem is a quantum mechanical analog of detection of a known signal in Gaussian noise. The quantum detection counterpart is formulated in terms of a pair of density operators and a solution is shown to exist. A perturbation solution is obtained by making use of a reproducing kernel Hilbert space of entire functions. The solution is particularly applicable to optical frequencies, where the effect of thermal radiation is small, and it is shown to converge to known results at zero thermal radiation. Curves are generated showing the detectability limit at optical frequencies. Also considered is the problem of finding an operator that maximizes a signal-to-noise ratio, defined for quantum detection in analogy with the classical theory. For a coherent signal with random phase, the operator that maximizes the signal-to-noise ratio is identicial to the one obtained by applying the Neyman Pearson criterion, thereby establishing a complete analogy with the classical detection theory. For a signal with known phase, however, the analogy breaks down in the limit of zero thermal radiation. In that case, it is shown that an operator that maximizes the classical signal-to-noise ratio does not exist.A part of this paper has been submitted to the University of California, Los Angeles, in partial satisfaction of the Ph.D. requirement.     

单模费米热噪声信道量子容量的估计

从量子信道的算符求和表象出发,对单模费米系统量子信道进行了参数化.参数化的结果得到另一类费米热噪声量子信道.给出了两类费米热噪声量子信道上相干信息的最大值,以估计信道的量子容量. 关键词： 量子容量 相干信息 费米热噪声信道     

Quantum Information in the Frame of Coherent States Representation

In this paper we have showed that the qubit can be expressed through the coherent states. Consequently, a message, i.e. a sequence of qubits, is expressed as a tensor product of coherent states. In the quantum information theory and practice, only the code and key message are expressed as a sequence of qubits, i.e. through a quantum channel, the properly information will be transmitted by using a classical channel. Even if the most used coherent states in the quantum information theory are the coherent states of the harmonic oscillator (particularly, expressing by them the Schrödinger “cat states” and the Bell states), several authors have been demonstrated that other kind of coherent states may be used in quantum information theory. For the ensembles of qubits, we must use the density operator, in order to describe the informational content of the ensemble. The diagonal representation of the density operator, in the coherent state representation, is also useful to examine the entanglement of the states.     

Radiation noise of an active interferometer

 An investigation of the behaviour of amplitude and frequency noise of radiation of an active interferometer in the regime of amplified optical bistability is presented. The phenomenon of non-amplification of external signal noise at sharp amplification of the external signal is established. The impact of strong amplitude fluctuations is studied. Our results have shown that the active interferometer allows an effective separation of the valid signal from the amplitude noise. The spectral density of a fluctuation of the field frequency in the active interferometer is shown to fall sharply in comparison with the “quantum limit”. The linewidth of radiation is determined by the spectral density at zero frequency and is equal to the natural linewidth of the external signal. The influence of quantum noise of the amplifying and absorbing media of the active interferometer is discussed. Received: 26 January 1996     

Information theories for time-dependent harmonic oscillator

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.     

Pseudoharmonic oscillator and their associated Gazeau–Klauder coherent states

In the paper we have constructed and examined the properties of the Gazeau–Klauder coherent states (GK-CSs) for the pseudoharmonic oscillator (PHO), one of three possible kinds in order to define the coherent states for this oscillator potential. In the second part, we have examined some nonclassical properties of these states. Our attention has been concentrated on the mixed states (thermal states). The diagonal P-representation of the corresponding density operator and some thermal expectations for the quantum canonical ideal gas of pseudoharmonic oscillators have also been examined. Like the CSs for the harmonic oscillator (HO), the GK-CSs for the PHO can be useful in the quantum information theory (QIT).     

Logarithm Versus Square Root： Comparing Quantum Fisher Information

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.     

Metric of States

Metric of quantum states plays an important role in quantum information theory. In this letter, we find the deep connection between quantum logic theory and quantum information theory. Using the method of quantum logic, we can get a famous inequality in quantum information theory, and we answer a question raised by S. Gudder.     

Quantum detection and estimation theory

A review. Quantum detection theory is a reformulation, in quantum-mechanical terms, of statistical decision theory as applied to the detection of signals in random noise. Density operators take the place of the probability density functions of conventional statistics. The optimum procedure for choosing between two hypotheses, and an approximate procedure valid at small signal-to-noise ratios and called threshold detection, are presented. Quantum estimation theory seeks best estimators of parameters of a density operator. A quantum counterpart of the Cramér-Rao inequality of conventional statistics sets a lower bound to the mean-square errors of such estimates. Applications at present are primarily to the detection and estimation of signals of optical frequencies in the presence of thermal radiation.This paper was prepared under grant NGR-05-009-079 from the National Aeronautics and Space Administration.     

Radiation field eigenstates and its unitary equivalence to coordinate eigenstates

In this paper, we reconstruct the explicit representation of the radiation field eigenstates in Fock space by decomposing the normally ordered Gaussian operator. Then with the help of the technique of integration within an ordered product of operators, the phase-shifting operator in quantum optics has been expressed through the Dirac's representation theory. In addition, the unitarily equivalent relation between the radiation field eigenstates and the coordinate eigenstates has been naturally established by the phase-shifting operator in quantum optics. These results deepen people's understanding to the radiation field eigenstates and phase-shifting operator in quantum optics.     

Experimental demonstration of a classical analog to quantum noise cancellation for use in gravitational wave detection

We present results that are a classical analog to quantum noise cancellation. It is possible to breach the standard quantum limit in an interferometer by the use of squeezing to correlate orthogonal quadratures of quantum noise, causing their effects on the resulting sensitivity to cancel. A laser beam incident on a Fabry-Perot cavity was imprinted with classical, correlated noise in the same quadratures that cause shot noise and radiation pressure noise. Couplings between these quadratures due to a movable mirror, sensitive to radiation pressure, cause the excess classical noise to cancel. This cancellation was shown to improve the signal to noise ratio of an injected signal by approximately a factor of 10.     

Quantum games entropy

We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There exists a strong relationship between game theories, information theories and statistical physics. The density operator and entropy are the bonds between these theories. The analysis we propose is based on the properties of entropy, the amount of information that a player can obtain about his opponent and a maximum or minimum entropy criterion. The natural trend of a physical system is to its maximum entropy state. The minimum entropy state is a characteristic of a manipulated system, i.e., externally controlled or imposed. There exist tacit rules inside a system that do not need to be specified or clarified and search the system equilibrium based on the collective welfare principle. The other rules are imposed over the system when one or many of its members violate this principle and maximize its individual welfare at the expense of the group.     

On the noise operator approach to quantized dissipative systems

Invoking complex classical coordinates and momenta a consistent Hamiltonian theory suitable for the quantization of dissipative systems has been developed previously. In another paper this formalism has been illustrated on the basis of a simple order parameter equation by means of density operator techniques. This quite naturally calls for a comparison with quantum noise operator techniques. The present paper is an attempt to satisfy these demands. Extensive use will be made of operator ordering techniques and quasi-classical Fokker-Planck equations. As before, a certain incompleteness in the extractable information is clearly exhibited. It will be observed that the two techniques do not produce similar results in a general dynamical state as a consequence of dissipation. However, in the stationary state and within certain approximations both methods do lead to identical conclusions for the order parameters statistics. It will be argued that within the present context in general noise operator techniques are to be favoured.     

Density Operator in Terms of Coherent States Representation with the Applications in the Quantum Information

In the quantum information theory operates with qubits and N-qubits that can be express through coherent states. Density operator admits a representation in terms of coherent states formalism. Consequently, in this paper the notions of qubit and density operators are described in the framework of coherent states. We have expressed a qubit as a coherent state, and thus a sequence of qubits becomes the tensor product of the coherent states. For the ensembles of qubits, it could be used the density operator, in order to describe the informational content of the ensemble. The coherent states representation may play an important role in the quantum information theory and the use of this formalism is not only theoretical, but also, due to its applications, of some practical relevance.     

热辐射中存在偶极相互作用的原子量子态保真度研究

建立了两个两能级原子置于热辐射场环境中的模型,当计及原子偶极间的相互作用时,利用密度矩阵方法,得到两能级原子密度矩阵元随时间的演化规律.针对三种不同的初始状态,分析置于强热辐射场中原子量子态保真度.结果表明:两个原子初始处于不同量子叠加态,量子信息在传输过程中可能发生部分失真,也可能不失真.初始状态对量子信息失真的快慢程度有明显的影响.     

The quantum origins of the free induction decay signal and spin noise

Experiments are described that elucidate the quantum mechanical origins of the free induction decay voltage and of spin noise. It is shown that the experimentally measured FID voltage induced in a Hertzian loop receiving coil following a 90 degrees pulse is typically two orders of magnitude too large to be accounted for by the current quantum theory of signal reception-coherent spontaneous emission. An experiment is then presented in which spin noise is easily observed in a circuit with a Q-factor of order unity, thereby undermining a popular hypothesis that such noise is due to spontaneous emission and is only observable because of the enhancement in the density of the radiation field in a high Q-factor tuned circuit, the NMR probe. Both the free induction decay and the spin noise are shown to be accurately predicted by near-field Faraday induction, which is described in the theory of quantum electrodynamics by an exchange of virtual photons. A heuristic approach to understanding the nature and role of virtual photons in the signal reception process is then given. Thus current popular statements that observation of the magnetic resonance phenomenon relies on the absorption and emission of radio waves are shown to be wrong.     

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.     

光场压缩态的产生及其在亚散粒噪声光学测量和量子信息中的应用

光场压缩态是一种非经典光场,它在超标准量子极限（SQL）的高精度光学测量、超低噪声光通信及量限通信等有着广泛应用前景,是物理学和信息科学交叉前沿研究课题,文章介绍了光场压缩态的产生及它在亚散粒噪声光学测量（sub-shot-noise=limit opical measurement）和量子信息中的重要应用。     

On the Similarity of the Statistical Characteristics of Spontaneous Radiation of a Quantum Amplifier at Different Gain Factors

The transformation laws governing the statistical properties of the quantum noise of an optical amplifier when its gain factor and spectral line profile are varied are considered. The correlation functions of quantum noise both at the amplifier output and after nonlinear transformation normalized to the correlation time of quantum noise at the amplifier output were found to be independent of the amplifier gain provided that it exceeds 10 for the Gaussian spectral line profile and 10³ for the Lorentzian profile. The spectral density of quantum noise transformed in a nonlinear system was shown to possess the same similarity property. It was found that the statistical characteristics possess a similarity property even in the case of variation of the spectral line profile from Gaussian to Lorentzian. It was concluded that such a characteristic of quantum noise of an optical amplifier as the correlation time bears virtually all information on the above-mentioned statistical properties at a reasonably large amplifier gain. The similarity property revealed has an important application. It allows finding the matching condition between the optical signal spectrum and the gain profile of the optical quantum amplifier to achieve the highest sensitivity of signal detection by the amplifier.     

强热辐射环境中两能级原子量子态保真度

两个两能级原子置于强热辐射场环境中，原子用泡利算符描述，环境用无穷的谐振子热库描述，运用密度矩阵方法，得到两能级原子密度矩阵元演化规律.针对三种不同的初始状态，分析置于热辐射场中原子量子态保真度.结果表明：当两个原子初始处于不同量子叠加态时，量子信息在传输过程中可能发生部分失真，也可能不失真. 关键词： 热辐射场 两能级原子 保真度 消相干