6,490 research outputs found
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 in terms of the fidelity of recovery (FoR), i.e., the maximal fidelity of the state with a state reconstructed from its marginal by acting only on the 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
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