Showing papers on "Quantum state published in 1978"

Optical communication with two-photon coherent states--Part I: Quantum-state propagation and quantum-noise

Abstract: Recent theoretical work has shown that novel quantum states, called two-photon coherent states (TCS), have significant potential for improving free-space optical communications. The first part of a three-part study of the communication theory of TCS radiation is presented. The issues of quantum-field propagation and optimum quantum-state generation are addressed. In particular, the quantum analog of the classical paraxial diffraction theory for quasimonochromatic scalar waves is developed. This result, which describes the propagation of arbitrary quantum states as a boundary-value problem suitable for communication system analysis, is used to treat a number of quantum transmitter optimization problems. It is shown that, under near-field propagation conditions, a TCS transmitter maximizes field-measurement signal-to-noise ratio among all transmitter quantum states; the performance of the TCS system exceeds that for a conventional (coherent state) transmitter by a factor of N_{s} + 1 , where N_{s} is the average number of signal photons (transmitter energy constraint). Under far-field propagation conditions, it is shown that use of a TCS local oscillator in the receiver can, in principle, attenuate field-measurement quantum noise by a factor equal to the diffraction loss of the channel, if appropriate spatial mode mixing can be achieved. These communcation results are derived by assuming that field-quadrature quantum measurement is performed. In part II of this study, photoemissive reception of TCS radiation will be considered; it will be shown therein that homodyne detection of TCS fields can realize the field-quadrature signal - to-noise ratio performance of part I. In part III, the relationships between photoemissive detection and general quantum measurements will be explored. In particular, a synthesis procedure will be obtained for realizing all the measurements described by arbitrary TCS.

Stationary States of Quantum Dynamical Semigroups

Abstract: We study the class of stationary states and the domain of attraction of each of them, for a dynamical semigroup possessing a faithful normal stationary state. We give applications to the approach to stationarity of an open quantum system, and to models of the quantum measurement process.

Open quantum systems with time-dependent Hamiltonians and their linear response

Abstract: We give a rigorous (Hamiltonian) treatment of a quantum system weakly coupled to an infinite free reservoir and subject to an external time-dependent driving potential varying on the scale of dissipation. The linear response of the system initially in thermal equilibrium is determined and compared with the usual expressions of linear response theory.

Relativistic quantum mechanics: A space-time formalism for spin-zero particles

Abstract: A single-particle quantum formalism is constructed for spin-zero particles based upon state functions and operators defined on a four-dimensional space-time manifold. This yields a generalized Schrodinger equation having a Hermitian Hamiltonian and a derivative with respect to proper time. This formulation requires that particle mass be treated as an observable, not as a specified constant. A consistent probability interpretation results and a proper classical limit is exhibited. It is proposed that this formalism should properly replace the conventional Klein-Gordon formalism.

Quantum Statistics of Homodyne and Heterodyne Detection

Abstract: There are three basic techniques that may be employed to detect optical radiation: photon detection, homodyne detection, and heterodyne detection (see Fig. 1). From the photocounting theory of Kelley and Kleiner [1], one can readily show that photon detection, in the limit of unity quantum efficiency, can be interpreted as the quantum measurement of the total photon number operator N for any quantum state of a quasi-monochromatic input field. No similar quantum description is as yet available for homodyne or heterodyne detection. In this paper, we shall derive the abstract quantum description of homodyne detection. Because heterodyne detection involves the more complicated concept of simultaneous measurement of non-commuting observables, its quantum description will only be briefly discussed.

Algebraic aspects of the Wigner distribution in quantum mechanics

Abstract: The algebraic structure underlying the method of the Wigner distribution in quantum mechanics and the Weyl correspondence between classical and quantum dynamical variables is analysed. The basic idea is to treat the operators acting on a Hilbert space as forming a second Hilbert space, and to make use of certain linear operators on them. The Wigner distribution is also related to the diagonal coherent state representation of quantum optics by this method.

Quantum theory and Hilbert space

Abstract: Two theorems are proven which show that any orthomodular partially ordered set (hence, in particular, the orthologic of questions on a physical system) can be embedded in the lattice of closed subspaces of a Hilbert space in such a way that the standard trace formula of quantum theory can be used to calculate all probabilities. Possible conclusions from these results and from the existence of counterexamples to stronger conjectures are then discussed.

A deterministic interpretation of the commutation and uncertainty relations of quantum theory and a redefinition of Planck’s constant as a coupling condition

Abstract: In a previous paper, a deterministic account of the dynamics underlying the quantum-mechanical wave amplitude equation (Schrodinger’s equation) was given. In the present paper, that topological analysis is extended to a deterministic interpretation of the commutation relations of quantum theory and Planck’s constant is redefined as a resonance coupling condition for linearly progressing and circularly orbiting particles. In the case of parametric excitation coupling of two linearly progressing particles, a temporal coupling condition is required, not Planck’s constant. It is demonstrated that, when described in four-parameter form, quantum-mechanical systems behave in a way identical to the hypercomplex systems called, by Hamilton, quaternions. The analysis provides a physical picture of quantum mechanics and quantum electrodynamics.

Thermochemical properties of atoms and molecules in specific quantum states

Abstract: Procedures are described for computing thermochemical properties in the ideal gas state for atoms and molecules in specific quantum states, and in thermal or nonthermal distributions over specific groups of quantum states. Formulas are given to generate values in the JANAF‐compatible format. Applications to electronic states of atoms, vibrational and vibration–rotational states of diatomic molecules, and vibrational states of polyatomic molecules are given as illustrations. It is shown that the choice of procedure for obtaining partition functions has only a minor effect upon the accuracy of the results, the major factors being the energy of the specified state(s) and the accuracy to which the heat of formation of the species itself is known. Procedures are developed for describing systems in which species in specified quantum states are considered together with the same species in a Boltzmann internal distribution, and for expressing the thermochemical properties of state‐selected species as polynomials ...

Joint Distributions of Observables on Quantum Logics

Abstract: A joint distribution of a set of observables on a quantum logic in a statem is defined and its properties are derived. It is shown that if the joint distribution exists, then the observables can be represented in the statem by a set of commuting operators on a Hilbert space.

Copenhagenism and Popperism

Abstract: There seems to be an unbridgeable gap between rival interpretations of quantum mechanics. One school speaks of the quantum state vector (and hence of the associated probabilities) as a property of individual quantum systems; another school insists that the quantum state vector is an ensemble property and that the associated probabilities refer to statistical distributions within the ensemble. The former school asserts that an observable of a system has a value in that system if and only if the appropriate observations have been made; the latter school claims that an observable always has a value in the system, though we may not always know it. The one school insists upon using quantum measurements for predictions only; the other for retrodictions also. The first school regards the discovery of the existence of non-commuting observables as placing restrictions upon the precision of our measurements (and hence upon the possible existence of a system with precisely defined values of the noncommuting observables); the second school maintains that these restrictions are of a statistical nature, limiting the precision not of our measurements of a system's observables, but only of our predictions about them. Despite all this, I claim that the differences are fundamentally linguistic at least in this sense: (i) there exist two possible definitions of 'state' for an individual system-definitions which coalesce in a classical deterministic theory, but which must be differentiated in an indeterministic theory of

Classical theory of radiative transitions

Abstract: A semiclassical method of approach to the origin of radiation in a simple quantum transition is reinterpreted and extended. The resulting concepts are applied to an analysis of the Compton effect, yielding the Klein-Nishina formula as usual. More significant is the natural appearance in this case of photonlike behavior of the purely classical electromagnetic fields. The same phenomenon can be hypothesized to occur in any transition in which a quantized-photon nature of radiation appears evident. A similar classical viewpoint taken toward the Lamb shift leads to a straightforward explanation which seems to give very good agreement with experiment. The calculated frequency for the $2{P}_{\frac{1}{2}}\ensuremath{\rightarrow}2{S}_{\frac{1}{2}}$ transition in H is 1064.57 MHz = 0.0355102 ${\mathrm{cm}}^{\ensuremath{-}1}$. The argument also has some important implications for ideas about the physical nature of quantum states.

Collective quantum states in model chemical systems

Abstract: Phenomenological field equations that describe isothermal chemical kinetics are cast into Hamiltonian form. The formalism is applied to a model reaction with autocatalytic chemicals in an extensive solution of substrate. Transforming the Hamiltonian into a collective representation shows that the autocatalytic subsystem can exist as a localized object with a discrete negative energy spectrum. It is observed that the collective state of matter exemplified by the model system also applies to other hypothetical reactions.

An Assumption in the Interpretation of Quantum Mechanics

Abstract: 'In the ontological models framework [Harrigan & Spekkens 2007], it is assumed that the probability measure representing a quantum state is independent of the choice of future measurement setting.' (Leifer 2014, 140) In this recently-unearthed piece I discuss a version of the above assumption, concluding that it is 'very difficult to justify on metaphysical grounds'. I note that abandoning it has an interesting potential payoff, given its crucial role in the no-go theorems of Bell and of Kochen & Specker. There has been increased interest in this option in recent years, under the label of retrocausal models of QM (see, e.g., Price & Wharton 2015, Wharton & Argaman 2020). The present piece may be of interest to diligent historians of this approach. It was written in 1978, while I was a graduate student in Cambridge.

The Hilbert Space Formulation of Quantum Physics

Abstract: In this chapter, we introduce the basic concepts of quantum theory. In Section 1.1, the state-space of a quantum physical system, the Hilbert space, is presented in axiomatic form and the concept of a closed linear manifold (subspace) is defined. In Section 1.2, we investigate the algebra of the subspaces of a Hilbert space and show that these subspaces form an orthocomplemented quasimodular lattice, which, moreover, has some additional properties. Closed linear manifolds are very closely related to projection operators, which are introduced in Section 1.3. On the other hand, projection operators represent observable quantities of the physical system. A physical system is characterized by its state and by its properties. These concepts will be defined in Section 1.4, and their relations to the elements and the subspaces of Hilbert space will be established.