An important primitive for quantum networking is entanglement distillation, whose goal is to enhance the fidelity of entangled qubits through local operations and classical communication (LOCC). Existing distillation protocols assume the availability of ideal, noiseless, communication channels. In this paper, we study the case in which communication takes place over noisy binary symmetric channels. We propose to implement local processing through parameterized quantum circuits (PQCs) that are optimized to maximize the average fidelity, while accounting for communication errors. The introduced approach, Noise Aware-LOCCNet (NA-LOCCNet), is shown to have significant advantages over existing protocols designed for noiseless communications.

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional programmable quantum processor, making it important to develop optimal approximate simulation techniques. In this paper, we study the challenging setting in which the channel to be simulated varies adversarially with time. We propose the use of matrix exponentiated gradient descent (MEGD), an online convex optimization method, and analytically show that it achieves a sublinear regret in time. Through experiments, we validate the main results for time-varying dephasing channels using a programmable generalized teleportation processor.

This paper studies distributed Bayesian learning in a setting encompassing a central server and multiple workers by focusing on the problem of mitigating the impact of stragglers. The standard one-shot, or embarrassingly parallel, Bayesian learning protocol known as consensus Monte Carlo (CMC) is generalized by proposing two straggler-resilient solutions based on grouping and coding. Two main challenges in designing straggler-resilient algorithms for CMC are the need to estimate the statistics of the workers' outputs across multiple shots, and the joint non-linear post-processing of the outputs of the workers carried out at the server. This is in stark contrast to other distributed settings like gradient coding, which only require the per-shot sum of the workers' outputs. The proposed methods, referred to as Group-based CMC (G-CMC) and Coded CMC (C-CMC), leverage redundant computing at the workers in order to enable the estimation of global posterior samples at the server based on partial outputs from the workers. Simulation results show that C-CMC may outperform G-CMC for a small number of workers, while G-CMC is generally preferable for a larger number of workers.

Large gains in the rate of cache-aided broadcast communication are obtained using coded caching, but to obtain this most existing centralized coded caching schemes require that the files at the server be divisible into a large number of parts (this number is called subpacketization). In fact, most schemes require the subpacketization to be growing asymptotically as exponential in √[\leftroot -1\uproot 1r]K for some positive integer r and K being the number of users. On the other extreme, few schemes having subpacketization linear in K are known; however, they require large number of users to exist, or they offer only little gain in the rate. In this work, we propose two new centralized coded caching schemes with low subpacketization and moderate rate gains utilizing projective geometries over finite fields. Both the schemes achieve the same asymptotic subpacketization, which is exponential in O((logK)2) (thus improving on the √[\leftroot -1\uproot 1r]K exponent). The first scheme has a larger cache requirement but has at most a constant rate (with increasing K), while the second has small cache requirement but has a larger rate. As a special case of our second scheme, we get a new linear subpacketization scheme, which has a more flexible range of parameters than the existing linear subpacketization schemes. Extending our techniques, we also obtain low subpacketization schemes for other multi-receiver settings such as distributed computing and the cache-aided interference channel. We validate the performance of all our schemes via extensive numerical comparisons. For a special class of symmetric caching schemes with a given subpacketization level, we propose two new information theoretic lower bounds on the optimal rate of coded caching.

Coded caching was introduced as a technique of systematically exploiting locally available storage at the clients to increase the channel throughput via coded transmissions. Most known coded caching schemes in literature enable large gains in terms of the rate, however at the cost of subpacketization that is exponential in K1/r(K being the number of clients, r some positive integer). Building upon recent prior work for coded caching design via line graphs and finite-field projective geometries, we present a new scheme in this work which achieves a subexponential (in K) subpacketization of qO((log(q) K)2)rate ⊖ (K/log(q) K)2) , for large K, and the cached fraction M/N being upper bounded by a constant 2/qα-1(for some prime power q and constant α ≥ 2). Apart from this asymptotic improvement, we show that through some numerical comparisons that our present scheme has much lower subpacketization than previous comparable schemes, however with an increased rate and some increase in cache size required. For instance, we obtain practically relevant subpacketization levels such as 102-107-for 102-104number of clients. Leveraging prior results on adapting coded caching schemes for the error-free broadcast channel to device to device (D2D) networks, we obtain a low-subpacketization scheme for D2D networks also, and give numerical comparison for the same with prior work.

Coded Caching is a promising solution to reduce the peak traffic in broadcast networks by prefetching the popular content close to end users and using coded transmissions. One of the chief issues of most coded caching schemes in literature is the issue of large subpacketization, i.e., they require each file to be divided into a large number of subfiles. In this work, we present a coded caching scheme using line graphs of bipartite graphs in conjunction with projective geometries over finite fields. The presented scheme achieves a rate Θ(K/logqK) (K being the number of users, q is some prime power) with subexponential subpacketization qO((logq K)^2)when cached fraction is upper bounded by a constant (M/N ≤ 1/qα, for some positive integer α). Compared to earlier schemes, the presented scheme has a lower subpacketization (albeit possessing a higher rate). We also present a new subpacketization dependent lower bound on the rate for caching schemes in which each subfile is cached in the same number of users. Compared to the previously known bounds, this bound seems to perform better for a range of parameters of the caching system.

Coded caching schemes on broadcast networks with user caches help to offload traffic from peak times to off-peak times by prefetching information from the server to the users during off-peak times and thus serving the users more efficiently during peak times using coded transmissions. We consider the problem of secretive coded caching which was proposed recently, in which a user should not be able to decode any information about any file that the user has not demanded. We propose a new secretive coded caching scheme which has a lower average rate compared to the existing state-of-the-art scheme, for the same memory available at the users. The proposed scheme is based on exploiting the presence of common demands between multiple users.