Robustness of quantum Markov chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.Comment: 14 pages, no figures; not for the feeble-minde

Soft-sediment deformation below mammoth tracks at White Sands National Monument (New Mexico) with implications for biomechanical inferences from tracks

Implicit in any biomechanical analysis of tracks (footprints), whatever the animal, is the assumption that depth distribution within the track reflects the applied plantar pressure in some way. Here we describe sub-track deformation structures produced by Proboscidea (probably Mammuthus columbi) at White Sands National Monument (WHSA) in New Mexico. Patterns of sub-surface deformation are consistent with the plantar pressure data for modern Proboscidea, but do not reflect track morphology. Our work cautions against overinterpreting track topology of any large animal, including extinct animals such as sauropods, in terms of their biomechanics unless the subsurface stratigraphy and associated variation in shear strength is known

Achievable rates for the Gaussian quantum channel

We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.Comment: 12 pages, 4 eps figures, REVTe

Can sexual selection drive female life histories? A comparative study on Galliform birds

Sexual selection is an important driver of many of the most spectacular morphological traits that we find in the animal kingdom (for example see Andersson, 1994). As such, sexual selection is most often emphasized as

Quantum state merging and negative information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.Comment: 23 pages, 3 figure

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie

All Inequalities for the Relative Entropy

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$ of parties is always less than or equal to the relative entropy of the two original n-party states. This is the monotonicity of relative entropy. Using techniques from convex geometry, we prove that monotonicity under restrictions is the only general inequality satisfied by relative entropies. In doing so we make a connection to secret sharing schemes with general access structures. A suprising outcome is that the structure of allowed relative entropy values of subsets of multiparty states is much simpler than the structure of allowed entropy values. And the structure of allowed relative entropy values (unlike that of entropies) is the same for classical probability distributions and quantum states.Comment: 15 pages, 3 embedded eps figure

Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev.

Forages for Conservation and Improved Soil Quality

Forages provide several soil benefits, including reduced soil erosion, reduced water runoff, improved soil physical properties, increased soil carbon, increased soil biologic activity, reduced soil salinity, and improved land stabilization and restoration when grown continuously or as part of a crop rotation. Ongoing research and synthesis of knowledge have improved our understanding of how forages alter and protect soil resources, thus providing producers, policymakers, and the general public information regarding which forage crops are best suited for a specific area or use (e.g. hay, grazing or bioenergy feedstock). Forages can be produced in forestland, range, pasture, and cropland settings. These land use types comprise 86% of non-Federal United States rural lands (Table 12.1). In the United States, active forage production occurs on 22.6 million ha and is used for hay, haylage, grass silage, and greenchop (Table 12.2). Forages are used as cover crops in several production systems, and approximately 4.2 million ha were recently planted in cover crops (Table 12.3). Currently, the highest cover crop use rates, as a percentage of total cropland within a given state, occur in the northeastern United States. Globally, permanent meadows and pastures account for over 3.3 billion ha, greater than arable land and permanent crops combined (Table 12.4). Within all regions of the world, except Europe, permanent meadows and pastures are a greater proportion of land cover than permanent crops. Pasture management information and resources are available for countries around the world (FAO 2017a,b). As seen in Tables 12.1–12.4, forages are used globally and can provide soil benefits across varied soil and climate types

Scalar cosmological perturbations from inflationary black holes

We study the correction to the scale invariant power spectrum of a scalar field on de Sitter space from small black holes that formed during a pre-inflationary matter dominated era. The formation probability of such black holes is estimated from primordial Gaussian density fluctuations. We determine the correction to the spectrum by first deriving the Keldysh propagator for a massless scalar field on Schwarzschild-de Sitter space. Our results suggest that the effect is strong enough to be tested -- and possibly even ruled out -- by observations.Comment: 41 pages, 11 figures, published versio