Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable $Y$ (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only $\epsilon$ bits of information is leaked about a random variable $X$ (representing private information) that is correlated with $Y$. Denoting this quantity by $g_\epsilon(X,Y)$, we show that for perfect privacy, i.e., $\epsilon=0$, one has $g_0(X,Y)=0$ for any pair of absolutely continuous random variables $(X,Y)$ and then derive a second-order approximation for $g_\epsilon(X,Y)$ for small $\epsilon$. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution $P_{XY}$. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when $\epsilon$ is sufficiently small using the approximation formula derived for $g_\epsilon(X,Y)$.Comment: 20 pages. To appear in Springer-Verla

On the strong converses for the quantum channel capacity theorems

A unified approach to prove the converses for the quantum channel capacity theorems is presented. These converses include the strong converse theorems for classical or quantum information transfer with error exponents and novel explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz strong converse for the classical channel capacity theorems. We provide a new proof for the error exponents for the classical information transfer. A long standing problem in quantum information theory has been to find out the strong converse for the channel capacity theorem when quantum information is sent across the channel. We give the quantum error exponent thereby giving a one-shot exponential upper bound on the fidelity. We then apply our results to show that the strong converse holds for the quantum information transfer across an erasure channel for maximally entangled channel inputs.Comment: Added the strong converse for the erasure channel for maximally entangled inputs and corrected minor typo

Kaon pair production in proton-nucleus collisions at 2.83 GeV kinetic energy

The production of non-phi K+K- pairs by protons of 2.83 GeV kinetic energy on C, Cu, Ag, and Au targets has been investigated using the COSY-ANKE magnetic spectrometer. The K- momentum dependence of the differential cross section has been measured at small angles over the 0.2--0.9 GeV/c range. The comparison of the data with detailed model calculations indicates an attractive K- -nucleus potential of about -60 MeV at normal nuclear matter density at a mean momentum of 0.5 GeV/c. However, this approach has difficulty in reproducing the smallness of the observed cross sections at low K- momenta.Comment: 7 pages, 5 figures, 1 tabl

Entanglement can increase asymptotic rates of zero-error classical communication over classical channels

It is known that the number of different classical messages which can be communicated with a single use of a classical channel with zero probability of decoding error can sometimes be increased by using entanglement shared between sender and receiver. It has been an open question to determine whether entanglement can ever increase the zero-error communication rates achievable in the limit of many channel uses. In this paper we show, by explicit examples, that entanglement can indeed increase asymptotic zero-error capacity, even to the extent that it is equal to the normal capacity of the channel. Interestingly, our examples are based on the exceptional simple root systems E7 and E8.Comment: 14 pages, 2 figur

Momentum dependence of the phi-meson nuclear transparency

The production of phi mesons in proton collisions with C, Cu, Ag, and Au targets has been studied via the phi -> K+K- decay at an incident beam energy of 2.83 GeV using the ANKE detector system at COSY. For the first time, the momentum dependence of the nuclear transparency ratio, the in-medium phi width, and the differential cross section for phi meson production at forward angles have been determined for these targets over the momentum range of 0.6 - 1.6 GeV/c. There are indications of a significant momentum dependence in the value of the extracted phi width, which corresponds to an effective phi-N absorption cross section in the range of 14 - 21 mb.Comment: 9 pages, 5 figure

The production of K+K- pairs in proton-proton collisions at 2.83 GeV

Differential and total cross sections for the pp -> ppK+K- reaction have been measured at a proton beam energy of 2.83 GeV using the COSY-ANKE magnetic spectrometer. Detailed model descriptions fitted to a variety of one-dimensional distributions permit the separation of the pp -> pp phi cross section from that of non-phi production. The differential spectra show that higher partial waves represent the majority of the pp -> pp phi total cross section at an excess energy of 76 MeV, whose energy dependence would then seem to require some s-wave phi-p enhancement near threshold. The non-phi data can be described in terms of the combined effects of two-body final state interactions using the same effective scattering parameters determined from lower energy data.Comment: 12 pages, 12 figures, 3 table

Synchrotron oscillation effects on an rf-solenoid spin resonance

New measurements are reported for the time dependence of the vertical polarization of a 0: 97 GeV/c deuteron beam circulating in a storage ring and perturbed by an rf solenoid. The storage ring is the cooler synchrotron (COSY) located at the Forschungszentrum Julich. The beam polarization was measured continuously using a 1.5 cm thick carbon target located at the edge of the circulating deuteron beam and the scintillators of the EDDA detector. An rf solenoid mounted on the ring was used to generate fields at and near the frequency of the 1 - G gamma spin resonance. Measurements were made of the vertical beam polarization as a function of time with the operation of the rf solenoid in either fixed or continuously variable frequency mode. Using rf-solenoid strengths as large as 2.66 x 10(-5) revolutions/turn, slow oscillations (similar to 1 Hz) were observed in the vertical beam polarization. When the circulating beam was continuously electron cooled, these oscillations completely reversed the polarization and showed no sign of diminishing in amplitude. But for the uncooled beam, the oscillation amplitude was damped to nearly zero within a few seconds. A simple spin-tracking model without the details of the COSY ring lattice was successful in reproducing these oscillations and demonstrating the sensitivity of the damping to the magnitude of the synchrotron motion of the beam particles. The model demonstrates that the characteristic features of measurements made in the presence of large synchrotron oscillations are distinct from the features of such measurements when made off resonance. These data were collected in preparation for a study of the spin coherence time, a beam property that needs to become long to enable a search for an electric dipole moment using a storage ring