Morton H. Rubin

Optimal staging of endoreversible heat engines

One way to classify performance indices of irreversible heat engines is according to how the indices change when one engine is replaced by two (or more) of the same kind in series. We investigate the performance of two endoreversible engines (i.e., heat engines with the only irreversibility being heat resistance to the surroundings) which are put in series to form a single engine, whose power output is maximized. In this unconstrained optimization the interface between the two stages, which for the present model is the intermediate temperature and the relative timing of the two engines, is arbitrary and can be used to satisfy other, nonthermodynamic constraints. Adding any constraint on the volume of the working gas does not lift this indeterminacy. The optimum composite system is equivalent to a single endoreversible engine, thus displaying a sequencing property similar to Carnot engines.

The generalized Carnot cycle: A working fluid operating in finite time between finite heat sources and sinks

The production of work in finite time from a reservoir with finite heat capacity is studied. A model system, for which the only irreversibilities result from finite rates of heat conduction, is adopted. The maximum work obtainable in finite time from such a system is derived, and is found to be strongly dependent upon the reservoir heat capacity. The cycle producing the maximum work is derived for an arbitrary one‐component working fluid; no equation of state is assumed. In the optimum cycle, when the working substance is in contact with a finite reservoir, then the temperature of the working fluid is an exponential function of time and the entropy of the working substance is a linear function of time. While the maximum work obtainable in a single fixed‐time cycle is a strictly increasing function of the reservoir heat capacity, the efficiency (work produced/heat put in) is a strictly decreasing function of the reservoir heat capacity, for the model system with a finite hot reservoir and an infinite cold ...

Interferometric Bell-state preparation using femtosecond-pulse-pumped spontaneous parametric down-conversion

We present a theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond-pulse-pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond-pulse-pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bell-state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond-pulse-pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.

Convexity and the separability problem of quantum mechanical density matrices

Abstract A finite-dimensional quantum mechanical system is modelled by a density ρ, a trace one, positive semi-definite matrix on a suitable tensor product space H[N]. For the system to demonstrate experimentally certain non-classical behavior, ρ cannot be in S, a closed convex set of densities whose extreme points have a specificed tensor product form. Two mathematical problems in the quantum computing literature arise from this context: 1. the determination whether a given ρ is in S, and 2. a measure of the “entanglement” of such a ρ in terms of its distance from S. In this paper we describe these two problems in detail for a linear algebra audience, discuss some recent results from the quantum computing literature, and prove some new results. We emphasize the roles of densities ρ as both operators on the Hilbert space H[N] and also as points in a real Hilbert space M. We are able to compute the nearest separable densities τ0 to ρ0 in particular classes of inseparable densities and we use the Euclidean distance between the two in M to quantify the entanglement of ρ0. We also show the role of τ0 in the construction of separating hyperplanes, so-called entanglement witnesses in the quantum computing literature.

Note on separability of the Werner states in arbitrary dimensions

Great progress has been made recently in establishing conditions for separability of a particular class of Werner densities on the tensor product space of n d-level systems (qudits). In this brief note we complete the process of establishing necessary and sufficient conditions for separability of these Werner densities by proving the sufficient condition for general n and d.

Complete separability and Fourier representations of n -qubit states

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and to emphasize its interpretation as a Fourier transform. We then prove a general sufficient condition for complete separability in terms of the spin coefficients and give necessary and sufficient conditions for the complete separability of a class of generalized Werner densities. As a further application of the theory, we give necessary and sufficient conditions for full separability for a particular set of n-qubit states whose densities all satisfy the Peres condition.

Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space

In tripartite discrete systems, two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger-Horne-Zeilinger (GHZ) class and the W class. To date, much research effort has been concentrated on the polarization entangled three-photon GHZ and W states. Most studies of continuous variable multiparticle entanglement have been focused on Gaussian states. In this Brief Report, we examine two classes of three-photon entangled states in space and time. One class is a three-mode three-photon entangled state and the other is a two-mode triphoton state. These states show behavior similar to the GHZ and W states when one of the photons is not detected. The three-mode entangled state resembles a W state, while a two-mode three-photon state resembles a GHZ state when one of the photons is traced away. We characterize the distinction between these two states by comparing the second-order correlation functions

First-order interference of nonclassical light emitted spontaneously at different times

G^{(2)}

Four photon interference experiment for the testing of the Greenberger-Horne-Zeilinger theorem

with the third-order correlation function

Ghost interference with optical parametric amplifier

G^{(3)}