Identifying the Information Gain of a Quantum Measurement

We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the measurement, if sufficient shared randomness is available. This result generalizes Winter's measurement compression theorem for fixed independent and identically distributed inputs [Winter, CMP 244 (157), 2004] to arbitrary inputs, and more importantly, it identifies the quantum mutual information of a measurement as the information gained by performing it, independent of the input state on which it is performed. Our result is a generalization of the classical reverse Shannon theorem to quantum-to-classical channels. In this sense, it can be seen as a quantum reverse Shannon theorem for quantum-to-classical channels, but with the entanglement assistance and quantum communication replaced by shared randomness and classical communication, respectively. The proof is based on a novel one-shot state merging protocol for "classically coherent states" as well as the post-selection technique for quantum channels, and it uses techniques developed for the quantum reverse Shannon theorem [Berta et al., CMP 306 (579), 2011].Comment: v2: new result about non-feedback measurement simulation, 45 pages, 4 figure

Converse bounds for private communication over quantum channels

This paper establishes several converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a "privacy test" to establish a general meta-converse bound for private communication, which has a number of applications. The meta-converse allows for proving that any quantum channel's relative entropy of entanglement is a strong converse rate for private communication. For covariant channels, the meta-converse also leads to second-order expansions of relative entropy of entanglement bounds for private communication rates. For such channels, the bounds also apply to the private communication setting in which the sender and receiver are assisted by unlimited public classical communication, and as such, they are relevant for establishing various converse bounds for quantum key distribution protocols conducted over these channels. We find precise characterizations for several channels of interest and apply the methods to establish several converse bounds on the private transmission capabilities of all phase-insensitive bosonic channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in IEEE Transactions on Information Theor

R\'enyi generalizations of quantum information measures

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in applications. We prescribe R\'enyi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {-1,0,1}. As examples, we describe R\'enyi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the R\'enyi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed R\'enyi conditional quantum mutual informations are monotone increasing in the R\'enyi parameter, and we have proofs of this conjecture for some special cases.Comment: 9 pages, related to and extends the results from arXiv:1403.610

The fidelity of recovery is multiplicative

© 1963-2012 IEEE. Fawzi and Renner recently established a lower bound on the conditional quantum mutual information (CQMI) of tripartite quantum states $ABC$ in terms of the fidelity of recovery (FoR), i.e., the maximal fidelity of the state $ABC$ with a state reconstructed from its marginal $BC$ by acting only on the $C$ system. The FoR measures quantum correlations by the local recoverability of global states and has many properties similar to the CQMI. Here, we generalize the FoR and show that the resulting measure is multiplicative by utilizing semi-definite programming duality. This allows us to simplify an operational proof by Brandão et al. of the above-mentioned lower bound that is based on quantum state redistribution. In particular, in contrast to the previous approaches, our proof does not rely on de Finetti reductions

Trigonometric Parallaxes for 1,507 Nearby Mid-to-Late M-dwarfs

The MEarth survey is a search for small rocky planets around the smallest, nearest stars to the Sun as identified by high proper motion with red colors. We augmented our planetary search time series with lower cadence astrometric imaging and obtained two million images of approximately 1800 stars suspected to be mid-to-late M dwarfs. We fit an astrometric model to MEarth's images for 1507 stars and obtained trigonometric distance measurements to each star with an average precision of 5 milliarcseconds. Our measurements, combined with the 2MASS photometry, allowed us to obtain an absolute K_s magnitude for each star. In turn, this allows us to better estimate the stellar parameters than those obtained with photometric estimates alone and to better prioritize the targets chosen to monitor at high cadence for planetary transits. The MEarth sample is mostly complete out to a distance of 25 parsecs for stars of type M5.5V and earlier, and mostly complete for later type stars out to 20 parsecs. We find eight stars that are within ten parsecs of the Sun for which there did not exist a published trigonometric parallax distance estimate. We release with this work a catalog of the trigonometric parallax measurements for 1,507 mid-to-late M-dwarfs, as well as new estimates of their masses and radii.Comment: ApJ, accepted. 36 pages, 8 figures, 2 tables. Please find our data table here: http://www.cfa.harvard.edu/MEarth/DataDR2.htm

A min-entropy uncertainty relation for finite size cryptography

Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for BB84 and six-state encodings. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove a new uncertainty relation in terms of the smooth min-entropy that is only marginally less strong, but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Renyi entropies that may be of independent interest.Comment: 5+6 pages, 1 figure, revtex. new version changed author's name from Huei Ying Nelly Ng to Nelly Huei Ying Ng, for consistency with other publication

Panchromatic spectral energy distributions of Herschel sources

Combining far-infrared Herschel photometry from the PACS Evolutionary Probe (PEP) and Herschel Multi-tiered Extragalactic Survey (HerMES) guaranteed time programs with ancillary datasets in the GOODS-N, GOODS-S, and COSMOS fields, it is possible to sample the 8–500 μm spectral energy distributions (SEDs) of galaxies with at least 7–10 bands. Extending to the UV, optical, and near-infrared, the number of bands increases up to 43. We reproduce the distribution of galaxies in a carefully selected restframe ten colors space, based on this rich data-set, using a superposition of multivariate Gaussian modes. We use this model to classify galaxies and build median SEDs of each class, which are then fitted with a modified version of the magphys code that combines stellar light, emission from dust heated by stars and a possible warm dust contribution heated by an active galactic nucleus (AGN). The color distribution of galaxies in each of the considered fields can be well described with the combination of 6–9 classes, spanning a large range of far- to near-infrared luminosity ratios, as well as different strength of the AGN contribution to bolometric luminosities. The defined Gaussian grouping is used to identify rare or odd sources. The zoology of outliers includes Herschel-detected ellipticals, very blue z ~ 1 Ly-break galaxies, quiescent spirals, and torus-dominated AGN with star formation. Out of these groups and outliers, a new template library is assembled, consisting of 32 SEDs describing the intrinsic scatter in the restframe UV-to-submm colors of infrared galaxies. This library is tested against L(IR) estimates with and without Herschel data included, and compared to eightother popular methods often adopted in the literature. When implementing Herschel photometry, these approaches produce L(IR) values consistent with each other within a median absolute deviation of 10–20%, the scatter being dominated more by fine tuning of the codes, rather than by the choice of SED templates. Finally, the library is used to classify 24 μm detected sources in PEP GOODS fields on the basis of AGN content, L(60)/L(100) color and L(160)/L(1.6) luminosity ratio. AGN appear to be distributed in the stellar mass (M_∗) vs. star formation rate (SFR) space along with all other galaxies, regardless of the amount of infrared luminosity they are powering, with the tendency to lie on the high SFR side of the “main sequence”. The incidence of warmer star-forming sources grows for objects with higher specific star formation rates (sSFR), and they tend to populate the “off-sequence” region of the M_∗ − SFR − z space