Related papers: Separating quantum communication and approximate r…
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the…
We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…
We study the communication complexity of linear algebraic problems over finite fields in the multi-player message passing model, proving a number of tight lower bounds. Specifically, for a matrix which is distributed among a number of…
We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
Quantum and private communications are affected by a fundamental limitation which severely restricts the optimal rates that are achievable by two distant parties. To overcome this problem, one needs to introduce quantum repeaters and, more…
We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple…
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved,…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum…
Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…
Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…
The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their $n$-bit…
The optimal rate of reliable communication over a quantum channel can be enhanced by pre-shared entanglement. Whereas the enhancement may be unbounded in infinite-dimensional settings even when the input power is constrained, a…
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among…
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the…
Following initial work by Gregoratti and Werner [J. Mod. Optics 50, 913-933, 2003 and quant-ph/0403092] and Hayden and King [quant-ph/0409026], we study the problem of the capacity of a quantum channel assisted by a "friendly (channel)…
We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is…
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady…