42 research outputs found

### Ultra-sensitive inertial sensors via neutral-atom interferometry

Upon looking at the various colossal interferometers, etc., discussed at this conference to test gravitational theory, one cannot avoid feeling that easier approaches exist. The use of low velocity, neutral atom matter waves in place of electromagnetic waves in sensitive inertial interferometer configurations is proposed. For applications, spacecraft experiments to sense a drag-free condition, to measure the Lense-Thirring precession, to measure the gravitomagnetic effect and/or the earth's geopotential (depending on altitude), and to detect long period gravitational waves are considered. Also, a terrestrial precision test of the equivalence principle on spin polarized atoms, capable of detecting effects of the 5th force is considered. While the ideas described herein are preliminary, the orders of magnitude are sufficiently tantalizing to warrant further study. Although existing proposed designs may be adequate for some of these experiments, the use of matter-wave interferometry offers reduced complexity and cost, and an absence of cryogenics

### Factoring and Fourier Transformation with a Mach-Zehnder Interferometer

The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for
factoring $N$ by means of an N-slit interference experiment is translated into
an experiment with a single Mach-Zehnder interferometer. With dispersive phase
shifters the ratio of the coherence length to wavelength limits the numbers
that can be factored. A conservative estimate permits $N \approx 10^7$. It is
furthermore shown, that sine and cosine Fourier coefficients of a real periodic
function can be obtained with such an interferometer.Comment: 5 pages, 2 postscript figures; to appear in Phys.Rev.A, Nov. 1997;
Figures contained only in replaced versio

### On the Numerical Determination of Relaxation and Retardation Spectra for Linearly Viscoelastic Materials

Knowledge of the relaxation spectrum is important because (1) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (2) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineering analyses. A numerical solution based on Simpson quadrature leads to an unstable solution in the sense that a decrease in integration intervals produces a progressively worse solution which oscillates between positive and negative values. This difficulty may be overcome by requiring that the curvature of the relaxation spectrum with respect to the relaxation times be minimized. The method is tested on the modified power law and good agreement with the exact and numerically determined relaxation spectrum is obtained. However, when the same method is used to determine the retardation spectrum, only the unstable solution is obtained, although the form of the integral equation is the same. This different behavior is attributed to the difference in the characteristics of the relaxation and retardation spectral functions

### Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Two separated observers, by applying local operations to a supply of
not-too-impure entangled states ({\em e.g.} singlets shared through a noisy
channel), can prepare a smaller number of entangled pairs of arbitrarily high
purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully
teleport unknown quantum states from one observer to the other, thereby
achieving faithful transfrom one observer to the other, thereby achieving
faithful transmission of quantum information through a noisy channel. We give
upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{\Psi^-}$)
distillable from mixed states $M$, showing $D(M)>0$ if
\bra{\Psi^-}M\ket{\Psi^-}>\half.Comment: 4 pages (revtex) plus 1 figure (postscript). See also
http://vesta.physics.ucla.edu/~smolin/ . Replaced to correct interchanged
$\sigma_x$ and $\sigma_z$ near top of column 2, page

### Mixed State Entanglement and Quantum Error Correction

Entanglement purification protocols (EPP) and quantum error-correcting codes
(QECC) provide two ways of protecting quantum states from interaction with the
environment. In an EPP, perfectly entangled pure states are extracted, with
some yield D, from a mixed state M shared by two parties; with a QECC, an arbi-
trary quantum state $|\xi\rangle$ can be transmitted at some rate Q through a
noisy channel $\chi$ without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state $\hat{M}(\chi)$ (obtained
by sharing halves of EPR pairs through a channel $\chi$) yields a QECC on
$\chi$ with rate $Q=D$, and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
$D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica-
tion, QECCs do not, and we prove Q is not increased by adding one-way classical
communication. However, both D and Q can be increased by adding two-way com-
munication. We show that certain noisy quantum channels, for example a 50%
depolarizing channel, can be used for reliable transmission of quantum states
if two-way communication is available, but cannot be used if only one-way com-
munication is available. We exhibit a family of codes based on universal hash-
ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models,
where S is the error entropy. We also obtain a specific, simple 5-bit single-
error-correcting quantum block code. We prove that {\em iff} a QECC results in
high fidelity for the case of no error the QECC can be recast into a form where
the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also
http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82
pages latex including 19 postscript figures included using psfig macro

### Theory of decoherence in a matter wave Talbot-Lau interferometer

We present a theoretical framework to describe the effects of decoherence on
matter waves in Talbot-Lau interferometry. Using a Wigner description of the
stationary beam the loss of interference contrast can be calculated in closed
form. The formulation includes both the decohering coupling to the environment
and the coherent interaction with the grating walls. It facilitates the
quantitative distinction of genuine quantum interference from the expectations
of classical mechanics. We provide realistic microscopic descriptions of the
experimentally relevant interactions in terms of the bulk properties of the
particles and show that the treatment is equivalent to solving the
corresponding master equation in paraxial approximation.Comment: 20 pages, 4 figures (minor corrections; now in two-column format

### Peaceful Coexistence: Examining Kent’s Relativistic Solution to the Quantum Measurement Problem

Can there be ‘peaceful coexistence’ between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit (i.e. the false assumption) in proofs of Bell inequalities as Outcome Independence would secure such peaceful coexistence: or, if not secure it, at least show a way—maybe the best or only way—to secure it. In this paper, I begin by being sceptical of Shimony’s approach, urging that we need a relativistic solution to the quantum measurement problem (Sect. 2). Then I analyse Outcome Independence in Kent’s realist one-world Lorentz-invariant interpretation of quantum theory (Sects. 3 and 4). Then I consider Shimony’s other condition, Parameter Independence, both in Kent’s proposal and more generally, in the light of recent remarkable theorems by Colbeck, Renner and Leegwater (Sect. 5). For both Outcome Independence and Parameter Independence, there is a striking analogy with the situation in pilot-wave theory. Finally, I will suggest that these recent theorems make some kind of peaceful coexistence mandatory for someone who, like Shimony, endorses Parameter Independence.Nagoya University, Graduate School of Information Science. Supported in part by the JSPS KAKENHI No. 26247016 and the John Templeton Foundation ID 35771

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