Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. We consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.Comment: v2: main results significantly generalized and improved; v3: extended to image-additive channels, change of title, journal versio

A Tight Upper Bound for the Third-Order Asymptotics for Most Discrete Memoryless Channels

This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n + O(1) if the epsilon-dispersion of the channel is positive. This matches a lower bound by Y. Polyanskiy (2010) for discrete memoryless channels with positive reverse dispersion. If the epsilon-dispersion vanishes, the logarithm of the epsilon-error capacity is upper bounded by the n times the capacity plus a constant term except for a small class of DMCs and epsilon >= 1/2.Comment: published versio

Second-Order Coding Rates for Channels with State

We study the performance limits of state-dependent discrete memoryless channels with a discrete state available at both the encoder and the decoder. We establish the epsilon-capacity as well as necessary and sufficient conditions for the strong converse property for such channels when the sequence of channel states is not necessarily stationary, memoryless or ergodic. We then seek a finer characterization of these capacities in terms of second-order coding rates. The general results are supplemented by several examples including i.i.d. and Markov states and mixed channels

The Third-Order Term in the Normal Approximation for the AWGN Channel

This paper shows that, under the average error probability formalism, the third-order term in the normal approximation for the additive white Gaussian noise channel with a maximal or equal power constraint is at least $\frac{1}{2} \log n + O(1)$. This matches the upper bound derived by Polyanskiy-Poor-Verd\'{u} (2010).Comment: 13 pages, 1 figur

Exactly solvable one-qubit driving fields generated via non-linear equations

Using the Hubbard representation for $SU(2)$ we write the time-evolution operator of a two-level system in the disentangled form. This allows us to map the corresponding dynamical law into a set of non-linear coupled equations. In order to find exact solutions, we use an inverse approach and find families of time-dependent Hamiltonians whose off-diagonal elements are connected with the Ermakov equation. The physical meaning of the so-obtained Hamiltonians is discussed in the context of the nuclear magnetic resonance phenomeno

Major Outcomes in Atrial Fibrillation Patients with One Risk Factor: Impact of Time in Therapeutic Range

BACKGROUND: The benefits and harms of oral anticoagulation (OAC) therapy in patients with only one stroke risk factor (i.e. CHA2DS2-VASc= 1 in males, or 2 in females) has been subject of debate. METHODS: We analysed all patients with only one stroke risk factor from the merged datasets of SPORTIF III and V trials. Anticoagulation control was defined according to time in therapeutic range (TTR). RESULTS: Of the original trial cohort, 1,097 patients had only one stroke risk factor. Stroke/systemic thromboembolic event had an incidence of 0.9 per 100 patient-years, with an incidence of 1.6 per 100 patient-years for all-cause death and 2.3%/patient-years for the composite outcome of stroke/systemic thromboembolic event/all-cause death. There were no significant differences in the risk for stroke/systemic thromboembolic event between sexes, nor between the different stroke risk factors amongst these atrial fibrillation patients with only one stroke risk factor. Cox regression analysis in patients treated with warfarin only found TTR to be inversely associated with stroke/systemic thromboembolic event (p=0.034) and all-cause death (p=0.015). Chronic heart failure was significantly associated with the outcome of all-cause death (p=0.0019) and the composite outcome of stroke/systemic thromboembolic event/all-cause death (p=0.021). There was a significant inverse linear association between TTR and the cumulative risk for both stroke/systemic thromboembolic event and all-cause death (both p<0.001). CONCLUSIONS: In atrial fibrillation patients with only one additional stroke risk factor (i.e. CHA2DS2-VASc= 1 in males or 2 in females), rates of major adverse events (stroke/systemic thromboembolic event, mortality) were high, despite anticoagulation. TTR in warfarin-treated patients was inversely associated with the occurrence of both stroke/systemic thromboembolic event and all-cause death

A band structure scenario for the giant spin-orbit splitting observed at the Bi/Si(111) interface

The Bi/Si(111) (sqrt{3} x sqrt{3})R30 trimer phase offers a prime example of a giant spin-orbit splitting of the electronic states at the interface with a semiconducting substrate. We have performed a detailed angle-resolved photoemission (ARPES) study to clarify the complex topology of the hybrid interface bands. The analysis of the ARPES data, guided by a model tight-binding calculation, reveals a previously unexplored mechanism at the origin of the giant spin-orbit splitting, which relies primarily on the underlying band structure. We anticipate that other similar interfaces characterized by trimer structures could also exhibit a large effect.Comment: 11 pages, 13 figure

Gate-tunable coherent perfect absorption of terahertz radiation in graphene

Perfect absorption of radiation in a graphene sheet may play a pivotal role in the realization of technologically relevant optoelectronic devices. In particular, perfect absorption of radiation in the terahertz (THz) spectral range would tremendously boost the utility of graphene in this difficult range of photon energies, which still lacks cheap and robust devices operating at room temperature. In this work we show that unpatterned graphene flakes deposited on appropriate substrates can display gate-tunable coherent perfect absorption (CPA) in the THz spectral range. We present theoretical estimates for the CPA operating frequency as a function of doping, which take into account the presence of common sources of disorder in graphene samples.Comment: To appear in 2D Material

Unbinding of mutually avoiding random walks and two dimensional quantum gravity

We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that unbinding in this model is a strong first order transition. The entropic exponents associated to denaturated loops and end-segments distributions show sharp differences at the transition point and in the high temperature phase. Their values can be deduced from some exact arguments relying on a conformal mapping of copolymer networks into a fluctuating geometry, i.e. in the presence of quantum gravity. An excellent agreement between analytical and numerical estimates is observed for all cases analized.Comment: 9 pages, 11 figures, revtex