The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information. This capacity can be expressed using ...the mutual information between input and output for a single use of the channel; although correlations between subsequent input bits are used to correct errors, they cannot increase the capacity. For quantum channels, it has been an open question whether entangled input states can increase the capacity to send classical information. The additivity conjecture states that entanglement does not help, making practical computations of the capacity possible. Although additivity is widely believed to be true, there is no proof. Here, we show that additivity is false, by constructing a random counter-example. Our results show that the most basic question of classical capacity of a quantum channel remains open, with further work needed to determine in which other situations entanglement can boost capacity.
Context.
Steady-state currents, so-called Eddington–Sweet circulation, result in the mixing of chemical elements in rotating stars, and in extreme cases lead to a homogeneous composition. Such ...circulation currents are also predicted in tidally deformed binary stars, which are thought to be progenitors of double black-hole merger events.
Aims.
This work aims to quantitatively characterise the steady-state circulation currents in components of a tidally locked binary system and to explore the effects of such currents on numerical models.
Methods.
Previous results describing the circulation velocity in a single rotating star and a tidally and rotationally distorted binary star are used to deduce a new prescription for the internal circulation in tidally locked binaries. We explore the effect of this prescription numerically with a detailed stellar evolution code for binary systems with initial orbital periods between 0.5 and 2.0 days, primary masses between 25 and 100
M
⊙
and initial mass-ratios
q
i
= 0.5, 0.7, 0.9, 1.0 at metallicity
Z
=
Z
⊙
/50.
Results.
When comparing circulation velocities in the radial direction for the cases of a single rotating star and a binary star, it is found that the average circulation velocity in the binary star may be described as an enhancement to the circulation velocity in a single rotating star. This velocity enhancement is a simple function depending on the masses of the binary components and amounts to a factor of approximately two when the components have equal masses. After applying this enhancement to stellar models, it is found that the formation of double helium stars through efficient mixing occurs for systems with higher initial orbital periods, lower primary masses and lower mass ratios, compared to the standard circulation scenario. Taking into account appropriate distributions for primary mass, initial period and mass ratio, models with enhanced mixing predict 2.4 times more double helium stars being produced in the parameter space than models without.
Conclusions.
We conclude that the effects of companion-induced circulation have strong implications for the formation of close binary black holes through the chemically homogeneous evolution channel. Not only do the predicted detection rates increase but double black-hole systems with mass ratios as low as 0.8 may be formed when companion-induced circulation is taken into account.
Structural rearrangements within single molecules occur on ultrafast time scales. Many aspects of molecular dynamics, such as the energy flow through excited states, have been studied using ...spectroscopic techniques, yet the goal to watch molecules evolve their geometrical structure in real time remains challenging. By mapping nuclear motions using femtosecond x-ray pulses, we have created real-space representations of the evolving dynamics during a well-known chemical reaction and show a series of time-sorted structural snapshots produced by ultrafast time-resolved hard x-ray scattering. A computational analysis optimally matches the series of scattering patterns produced by the x rays to a multitude of potential reaction paths. In so doing, we have made a critical step toward the goal of viewing chemical reactions on femtosecond time scales, opening a new direction in studies of ultrafast chemical reactions in the gas phase.
Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological ...quantum order for which the unperturbed Hamiltonian
H
0
can be written as a sum of local pairwise commuting projectors on a
D
-dimensional lattice. We consider a perturbed Hamiltonian
H
=
H
0
+
V
involving a generic perturbation
V
that can be written as a sum of short-range bounded-norm interactions. We prove that if the strength of
V
is below a constant threshold value then
H
has well-defined spectral bands originating from the low-lying eigenvalues of
H
0
. These bands are separated from the rest of the spectrum and from each other by a constant gap. The width of the band originating from the smallest eigenvalue of
H
0
decays faster than any power of the lattice size.
Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle ...solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.
We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground ...or stationary state correlation functions can be written as a piece decaying exponentially in space plus a term set by matrix elements between the low-lying states. The key to the proof is a local approximation to the negative energy, or annihilation, part of an operator in a gapped system. Applications to numerical simulation of quantum systems and to networks are discussed.
Community detection as an inference problem Hastings, M B
Physical review. E, Statistical, nonlinear and soft matter physics,
09/2006, Letnik:
74, Številka:
3 Pt 2
Journal Article
Recenzirano
Odprti dostop
We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that ...this leads to fast, accurate algorithms for community detection.
We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a ...flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of
e
2
/
h
, up to exponentially small corrections in the linear size
L
. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.
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