A Quantum Multiparty Packing Lemma and the Relay Channel

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be "packed" into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.Comment: 20 page

Locating Encrypted Data Hidden Among Non-Encrypted Data using Statistical Tools

This research tests the security of software protection techniques that use encryption to protect code segments containing critical algorithm implementation to prevent reverse engineering. Using the National Institute of Standards and Technology (NIST) Tests for Randomness encrypted regions hidden among non-encrypted bits of a binary executable file are located. The location of ciphertext from four encryption algorithms (AES, DES, RSA, and TEA) and three block sizes (10, 100, and 500 32-bit words) were tested during the development of the techniques described in this research. The test files were generated from the Win32 binary executable file of Adobe\u27s Acrobat Reader version 7.0.9. The culmination of this effort developed a technique capable of locating 100% of the encryption regions with no false negative error and minimal false positive error with a 95% confidence. The encrypted region must be encrypted with a strong encryption algorithm whose ciphertext appears statistically random to the NIST Tests for Randomness, and the size of the encrypted region must be at least 100 32-bit words (3,200 bits)

Entanglement Wedge Reconstruction via Universal Recovery Channels

We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.Comment: 16 pages, 3 figures. v4: Generalized approximate recovery of 2-point functions to arbitrary correlation functions. Clarified relation to previous work. Added Geoffrey Penington as co-autho

Holographic duality from random tensor networks

Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface topologically in a way similar to creation of a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by AdS/CFT duality, our main results define a more general form of bulk-boundary correspondence which could be useful for extending holography to other spacetimes.Comment: 57 pages, 13 figure

Environment-Assisted Error Correction of Single-Qubit Phase Damping

Open quantum system dynamics of random unitary type may in principle be fully undone. Closely following the scheme of environment-assisted error correction proposed by Gregoratti and Werner [M. Gregoratti and R. F. Werner, J. Mod. Opt. 50(6), 915-933 (2003)], we explicitly carry out all steps needed to invert a phase-damping error on a single qubit. Furthermore, we extend the scheme to a mixed-state environment. Surprisingly, we find cases for which the uncorrected state is closer to the desired state than any of the corrected ones

Searching for the signature of a pair density wave in YBa2_2Cu3_3O6.67_{6.67} using high energy X-ray diffraction

We have carried out a search for a pair density wave signature using high-energy X-ray diffraction in fields up to 16 T. We do not see evidence for a signal at the predicted wavevector. This is a report on the details of our experiment, with information on where in reciprocal space we looked.Comment: 5 pages, report on experimental result

EVLA Observations Constrain the Environment and Progenitor System of Type Ia Supernova 2011fe

We report unique EVLA observations of SN 2011fe representing the most sensitive radio study of a Type Ia supernova to date. Our data place direct constraints on the density of the surrounding medium at radii ~10^15-10^16 cm, implying an upper limit on the mass loss rate from the progenitor system of Mdot <~ 6 x 10^-10 Msol/yr (assuming a wind speed of 100 km/s), or expansion into a uniform medium with density n_CSM <~ 6 cm^-3. Drawing from the observed properties of non-conservative mass transfer among accreting white dwarfs, we use these limits on the density of the immediate environs to exclude a phase space of possible progenitors systems for SN 2011fe. We rule out a symbiotic progenitor system and also a system characterized by high accretion rate onto the white dwarf that is expected to give rise to optically-thick accretion winds. Assuming that a small fraction, 1%, of the mass accreted is lost from the progenitor system, we also eliminate much of the potential progenitor parameter space for white dwarfs hosting recurrent novae or undergoing stable nuclear burning. Therefore, we rule out the most popular single degenerate progenitor models for SN 2011fe, leaving a limited phase space inhabited by some double degenerate systems and exotic progenitor scenarios.Comment: Accepted to Ap

Tracing chemical evolution over the extent of the Milky Way's Disk with APOGEE Red Clump Stars

We employ the first two years of data from the near-infrared, high-resolution SDSS-III/APOGEE spectroscopic survey to investigate the distribution of metallicity and alpha-element abundances of stars over a large part of the Milky Way disk. Using a sample of ~10,000 kinematically-unbiased red-clump stars with ~5% distance accuracy as tracers, the [alpha/Fe] vs. [Fe/H] distribution of this sample exhibits a bimodality in [alpha/Fe] at intermediate metallicities, -0.9<[Fe/H]<-0.2, but at higher metallicities ([Fe/H]=+0.2) the two sequences smoothly merge. We investigate the effects of the APOGEE selection function and volume filling fraction and find that these have little qualitative impact on the alpha-element abundance patterns. The described abundance pattern is found throughout the range 5<R<11 kpc and 0<|Z|<2 kpc across the Galaxy. The [alpha/Fe] trend of the high-alpha sequence is surprisingly constant throughout the Galaxy, with little variation from region to region (~10%). Using simple galactic chemical evolution models we derive an average star formation efficiency (SFE) in the high-alpha sequence of ~4.5E-10 1/yr, which is quite close to the nearly-constant value found in molecular-gas-dominated regions of nearby spirals. This result suggests that the early evolution of the Milky Way disk was characterized by stars that shared a similar star formation history and were formed in a well-mixed, turbulent, and molecular-dominated ISM with a gas consumption timescale (1/SFE) of ~2 Gyr. Finally, while the two alpha-element sequences in the inner Galaxy can be explained by a single chemical evolutionary track this cannot hold in the outer Galaxy, requiring instead a mix of two or more populations with distinct enrichment histories.Comment: 18 pages, 17 figures. Accepted for publication in Ap