Related papers: Exponential Separation between Quantum Communicati…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that…
We consider the problem of covert communication with random slot selection over binary-input Discrete Memoryless Channels and Additive White Gaussian Noise channels, in which a transmitter attempts to reliably communicate with a legitimate…
Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements each of which requires only a finite number of rounds.…
Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices,…
In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set $\Theta(2^{n})$ bits with respect to classical…
The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…
We study the quantum-classical polynomial hierarchy, QCPH, which is the class of languages solvable by a constant number of alternating classical quantifiers followed by a quantum verifier. Our main result is that QCPH is infinite relative…
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
The reliability function gives the rate of exponential convergence to zero of the error probability in a communication channel. In this paper bounds for the reliability function of a quantum pure state channel are given, reminiscent of the…
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate…
The quadratic decaying property of the information rate function states that given a fixed conditional distribution $p_{\mathsf{Y}|\mathsf{X}}$, the mutual information between the (finite) discrete random variables $\mathsf{X}$ and…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
Lifting theorems are theorems that relate the query complexity of a function $f:\{0,1\}^{n}\to\{0,1\}$ to the communication complexity of the composed function $f \circ g^{n}$, for some "gadget" $g:\{0,1\}^{b}\times\{0,1\}^{b}\to\{0,1\}$.…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
We study a natural complexity measure of Boolean functions known as the rational degree. Denoted $\textrm{rdeg}(f)$, it is the minimal degree of a rational function that is equal to $f$ on the Boolean hypercube. For total functions $f$, it…
Finding exponential separation between quantum and classical information tasks is like striking gold in quantum information research. Such an advantage is believed to hold for quantum computing but is proven for quantum communication…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function…