Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels

Quantum entanglement can be used in a communication scheme to establish a correlation between successive channel inputs that is impossible by classical means. It is known that the classical capacity of quantum channels can be enhanced by such entangled encoding schemes, but this is not always the case. In this paper, we prove that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter. In doing so, we identify a bound on the strong converse exponent, which determines the exponentially decaying rate at which the success probability tends to zero, for a sequence of codes with communication rate exceeding capacity. Proving a strong converse, along with an achievability theorem, shows that the classical capacity is a sharp boundary between reliable and unreliable communication regimes. One of the main tools in our proof is the sandwiched Renyi relative entropy. The same method of proof is used to derive an exponential bound on the success probability when communicating over an arbitrary quantum channel assisted by classical feedback, provided that the transmitter does not use entangled encoding schemes.Comment: 24 pages, 2 figures, v4: final version accepted for publication in Problems of Information Transmissio

Quantum Channel Capacities Per Unit Cost

Communication over a noisy channel is often conducted in a setting in which different input symbols to the channel incur a certain cost. For example, for bosonic quantum channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a quantum channel such as classical communication, entanglement-assisted classical communication, private communication, and quantum communication. For each task, we define the corresponding capacity per unit cost and derive a formula for it analogous to that of the usual capacity. Furthermore, for the special and natural case in which there is a zero-cost state, we obtain expressions in terms of an optimized relative entropy involving the zero-cost state. For each communication task, we construct an explicit pulse-position-modulation coding scheme that achieves the capacity per unit cost. Finally, we compute capacities per unit cost for various bosonic Gaussian channels and introduce the notion of a blocklength constraint as a proposed solution to the long-standing issue of infinite capacities per unit cost. This motivates the idea of a blocklength-cost duality, on which we elaborate in depth.Comment: v3: 18 pages, 2 figure

Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.Comment: v2: 6 pages, 1 figure, final version published in conference proceeding

Temperature Dependent Piezoelectric Properties of Lead-Free (1-x)K0.6Na0.4NbO3–xBiFeO3 Ceramics

(1-x)K0.4Na0.6NbO3–xBiFeO3 lead-free piezoelectric ceramics were successfully prepared in a single perovskite phase using the conventional solid-state synthesis. Relative permittivity (εr) as a function of temperature indicated that small additions of BiFeO3 not only broadened and lowered the cubic to tetragonal phase transition (TC) but also shifted the tetragonal to orthorhombic phase transition (TO–T) toward room temperature (RT). Ceramics with x = 1 mol.% showed optimum properties with small and large signal piezoelectric coefficient, d33 = 182 pC/N and d∗33 = 250 pm/V, respectively, electromechanical coupling coefficient, kp = 50%, and TC = 355°C. kp varied by ∼5% from RT to 90°C, while d∗33 showed a variation of ∼15% from RT to 75°C, indicating that piezoelectric properties were stable with temperature in the orthorhombic phase field. However, above the onset of TO–T, the properties monotonically degraded in the tetragonal phase field as TC was approached

The mechanism for stochastic resonance enhancement of mammalian auditory information processing

BACKGROUND: In a mammalian auditory system, when intrinsic noise is added to a subthreshold signal, not only can the resulting noisy signal be detected, but also the information carried by the signal can be completely recovered. Such a phenomenon is called stochastic resonance (SR). Current analysis of SR commonly employs the energies of the subthreshold signal and intrinsic noise. However, it is difficult to explain SR when the energy addition of the signal and noise is not enough to lift the subthreshold signal over the threshold. Therefore, information modulation has been hypothesized to play a role in some forms of SR in sensory systems. Information modulation, however, seems an unlikely mechanism for mammalian audition, since it requires significant a priori knowledge of the characteristics of the signal. RESULTS: We propose that the analysis of SR cannot rely solely on the energies of a subthreshold signal and intrinsic noise or on information modulation. We note that a mammalian auditory system expends energy in the processing of a noisy signal. A part of the expended energy may therefore deposit into the recovered signal, lifting it over threshold. We propose a model that in a rigorous mathematical manner expresses this new theoretical viewpoint on SR in the mammalian auditory system and provide a physiological rationale for the model. CONCLUSION: Our result indicates that the mammalian auditory system may be more active than previously described in the literature. As previously recognized, when intrinsic noise is used to generate a noisy signal, the energy carried by the noise is added to the original subthreshold signal. Furthermore, our model predicts that the system itself should deposit additional energy into the recovered signal. The additional energy is used in the processing of the noisy signal to recover the original subthreshold signal

An extremal effective survey about extremal effective cycles in moduli spaces of curves

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.Comment: Submitted to the Proceedings of the Abel Symposium 2017. Comments are welcom

Simulation of chemical reaction dynamics on an NMR quantum computer

Quantum simulation can beat current classical computers with minimally a few tens of qubits and will likely become the first practical use of a quantum computer. One promising application of quantum simulation is to attack challenging quantum chemistry problems. Here we report an experimental demonstration that a small nuclear-magnetic-resonance (NMR) quantum computer is already able to simulate the dynamics of a prototype chemical reaction. The experimental results agree well with classical simulations. We conclude that the quantum simulation of chemical reaction dynamics not computable on current classical computers is feasible in the near future.Comment: 37 pages, 7 figure

Presenting a Labelled Dataset for Real-Time Detection of Abusive User Posts

Social media sites facilitate users in posting their own personal comments online. Most support free format user posting, with close to real-time publishing speeds. However, online posts generated by a public user audience carry the risk of containing inappropriate, potentially abusive content. To detect such content, the straightforward approach is to filter against blacklists of profane terms. However, this lexicon filtering approach is prone to problems around word variations and lack of context. Although recent methods inspired by machine learning have boosted detection accuracies, the lack of gold standard labelled datasets limits the development of this approach. In this work, we present a dataset of user comments, using crowdsourcing for labelling. Since abusive content can be ambiguous and subjective to the individual reader, we propose an aggregated mechanism for assessing different opinions from different labellers. In addition, instead of the typical binary categories of abusive or not, we introduce a third class of ‘undecided’ to capture the real life scenario of instances that are neither blatantly abusive nor clearly harmless. We have performed preliminary experiments on this dataset using best practice techniques in text classification. Finally, we have evaluated the detection performance of various feature groups, namely syntactic, semantic and context-based features. Results show these features can increase our classifier performance by 18% in detection of abusive content