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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Going through a quantum phase

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Shapiro, Jeffrey H.↗
NASA NTRS1994

Homodyning and heterodyning the quantum phase

The double-homodyne and the heterodyne detection schemes for phase shifts between two synchronous modes of the electromagnetic field are analyzed in the framework of quantum estimation theory. The probability operator-valued measures (POM's) of the detectors are evaluated and compared with the ideal one in the limit of strong local reference oscillator. The present operational approach leads to a reasonable definition of phase measurement, whose sensitivity is actually related to the output r.m.s. noise of the photodetector. We emphasize that the simple-homodyne scheme does not correspond to a proper phase-shift measurements as it is just a zero-point detector. The sensitivity of all detection schemes are optimized at fixed energy with respect to the input state of radiation. It is shown that the optimal sensitivity can be actually achieved using suited squeezed states.

Dariano, Giacomo M.↗
NASA NTRS1992

Algorithmic information theory and the hidden variable question

The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.

Fuchs, Christopher↗
NASA NTRS1983

A near-optimum receiver structure for the detection of M-ary optical PPM signals

A class of receivers called conditionally nulling receivers is defined for quantum noise limited optical communications. These receivers have the ability to decide at each moment in time whether or not to coherently combine a predetermined local oscillator field with the received optical field, prior to performing an energy measurement (photodetection) on the combined field. Conditionally nulling receivers are applicable to pulse position modulation and related modulation schemes, which have the property that, at each moment in time, the transmitted signal is in one of only two states, on or off. The local oscillator field which may or may not be added by the receiver is an exact replica of the negative of the received on field; hence, the receiver can exactly null the on signal if the on signal is present and the receiver chooses to use the local field. An ideal conditionally nulling receiver achieves very nearly the same error probability (within a multiplicative factor varying froom 1 to 2.15) as the optimum quantum measurement for quantum noise limited detection of M-ary PPM signals. In contrast, other known receiving methods, such as direct, heterodyne, and homodyne detection, are exponentially suboptimum.

Dolinar, S. J., Jr.↗
NASA NTRS1979

Experimental transition probabilities and Stark-broadening parameters of neutral and single ionized tin

Strengths and Stark-effect widths of the Sn I and Sn II lines prominent between 3200 and 7900 A are measured with a spectroscopic shock tube. Absolute strengths of 17 ionic lines are obtained with estimated (22-50)% accuracy and conform to appropriate quantum-mechanical sum rules. Relative transition probabilities for nine prominent neutral tin lines, normalized to radiative-lifetime data, are compared with other experiments and theoretical predictions. Parameters for Stark-effect broadening are measured over a range of plasma electron densities. Broadening data (with accuracies of 15-35%) for one neutral and ten ionic lines of tin are compared to theoretical predictions.

Miller, M. H.↗
NASA NTRS1971

The application of signal detection theory to optics

The restoration of images focused on a photosensitive surface is treated from the standpoint of maximum likelihood estimation, taking into account the Poisson distributions of the observed data, which are the numbers of photoelectrons from various elements of the surface. A detector of an image focused on such a surface utilizes a certain linear combination of those numbers as the optimum detection statistic. Methods for calculating the false alarm and detection probabilities are proposed. It is shown that measuring noncommuting observables in an ideal quantum receiver cannot yield a lower Bayes cost than that attainable by a system measuring only commuting observables.

Helstrom, C. W.↗
NASA NTRS1994

Pseudomaster equation for the no-count process in a continuous photodetection

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Lee, Ching-Tsung↗
NASA NTRS1992

Proposal for a QND which-path measurement using photons

A scheme is proposed for experimentally realizing the famous two-slit gedaenken experiment using photons. As elegantly discussed for electrons by Feynman, a particle's quantum pathways interfere to produce fringes in the probability density for the particle to be found at a particle location. If the path taken by the particle is experimentally determined, the complementarity principle says that the fringes must disappear. To carry out this experiment with photons is difficult because normally the act of determining a photon's location destroys it. We propose to overcome this difficulty by putting a type-2 optical parametric amplifier (OPA) in each arm of a Mach-Zehnder interferometer, and observing fringes at the output. An OPA responds to an input photon by increasing its probability to produce a pair of photons with polarization orthogonal to the input, the detection of which allows partial inference about the path taken by the input photon without destroying it. Thus, the measurement is of the quantum nondemolition (QND) type.

Raymer, M. G.↗
NASA NTRS1996

Physical Meaning of the Optimum Measurement Process in Quantum Detection Theory

The optimum measurement processes are represented as the optimum detection operators in the quantum detection theory. The error probability by the optimum detection operators goes beyond the standard quantum limit automatically. However the optimum detection operators are given by pure mathematical descriptions. In order to realize a communication system overcoming the standard quantum limit, we try to give the physical meaning of the optimum detection operators.

Osaki, Masao↗
NASA NTRS1992

Photoexcited escape probability, optical gain, and noise in quantum well infrared photodetectors

We present a detailed and thorough study of a wide variety of quantum well infrared photodetectors (QWIPs), which were chosen to have large differences in their optical and transport properties. Both n- and p-doped QWIPs, as well as intersubband transitions based on photoexcitation from bound-to-bound, bound-to-quasi-continuum, and bound-to-continuum quantum well states were investigated. The measurements and theoretical analysis included optical absorption, responsivity, dark current, current noise, optical gain, hot carrier mean free path; net quantum efficiency, quantum well escape probability, quantum well escape time, as well as detectivity. These results allow a better understanding of the optical and transport physics and thus a better optimization of the QWIP performance.

Levine, B. F.↗
NASA NTRS1985

Optical Quantum Receiver For Binary Signals

In quantum optical receiver, both amplitude and phase of received optical signal measured to extract as much information as possible, thereby reducing error probability. Phase-modulated received signal mixed with equal amplitude replica of optical carrier generated in phase locked loop. Two signals interfere with each other at photomultiplier cathode. Probability of error with this scheme close to theoretical minimum and implemented with current technology.

Vilnrotter, V. A.↗
NASA NTRS2005

Bidirectional Classical Stochastic Processes with Measurements and Feedback

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

Hahne, G. E.↗
NASA NTRS1992

Entropic uncertainty relation at finite temperature

We discussed how much information is lost when a particle is in equilibrium with the thermal reservoir of temperature T = 1/beta. The universal temperature correction to the r.h.s. of U(X,P:psi) greater than or = 1 + ln(pi) is determined. For this purpose, it is convenient to employ the framework of thermo-field dynamics (TFD). This formulation of finite-temperature (T not = 0) quantum theory utilizes the doubled Hilbert space, the normal operator (A) acting on the objective space, and its corresponding tildian operator on the fictitious space. The physical probability density associated with the measurement of the normal operator, A, is given, and the information entropy at T not = 0 is defined. The results describe how the thermal disturbance effects in S sub X or S sub P (delta X or delta P) can be suppressed by squeezing with keeping U = S sub X + S sub P (delta X x delta P) its minimum value.

Abe, Sumiyoshi↗
NASA NTRS1996

Decoherence and Exponential Law: A Solvable Model

We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.

Pascazio, Saverio↗
NASA NTRS2013

Partitioned-Interval Quantum Optical Communications Receiver

The proposed quantum receiver in this innovation partitions each binary signal interval into two unequal segments: a short "pre-measurement" segment in the beginning of the symbol interval used to make an initial guess with better probability than 50/50 guessing, and a much longer segment used to make the high-sensitivity signal detection via field-cancellation and photon-counting detection. It was found that by assigning as little as 10% of the total signal energy to the pre-measurement segment, the initial 50/50 guess can be improved to about 70/30, using the best available measurements such as classical coherent or "optimized Kennedy" detection.

Vilnrotter, Victor A.↗
NASA NTRS1978

CO2 photolysis revisited

Measurements have been made of the absolute oxygen atom yields from CO2 photolysis at 1470 and 1302-1306 A; in both cases the yield is unity. The CO generation rates have also been measured in these two wavelength regions, and they are proportional to the oxygen atom generation rates; by implication the CO quantum yields are thus also unity. The CO deficiencies observed in earlier work on this subject are probably caused by heterogenous processes.

Slanger, T. G.↗
NASA NTRS1992

A Gaussian measure of quantum phase noise

We study the width of the semiclassical phase distribution of a quantum state in its dependence on the average number of photons (m) in this state. As a measure of phase noise, we choose the width, delta phi, of the best Gaussian approximation to the dominant peak of this probability curve. For a coherent state, this width decreases with the square root of (m), whereas for a truncated phase state it decreases linearly with increasing (m). For an optimal phase state, delta phi decreases exponentially but so does the area caught underneath the peak: all the probability is stored in the broad wings of the distribution.

Schleich, Wolfgang P.↗