Related papers: Refuting the Direct Sum Conjecture for Total Funct…
We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\colon X\times Y \to \{0,1\}$ where each value is chosen to be 1 independently with probability…
Alice wants to send an arbitrary binary word to Bob. We show here that there is no problem for her to do that with only two bits. Of course, we consider here information like a signal in 4D.
Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…
In Direct Sum problems [KRW], one tries to show that for a given computational model, the complexity of computing a collection of finite functions on independent inputs is approximately the sum of their individual complexities. In this…
In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the one-way model to demonstrate an exponential classical-quantum communication separation. In this problem, Alice's…
This paper studies the one-way communication complexity of the subgroup membership problem, a classical problem closely related to basic questions in quantum computing. Here Alice receives, as input, a subgroup $H$ of a finite group $G$;…
We study the following combinatorial game played by two players, Alice and Bob, which generalizes the Pizza game considered by Brown, Winkler and others. Given a connected graph G with nonnegative weights assigned to its vertices, the…
We study two basic graph parameters, the chromatic number and the orthogonal rank, in the context of classical and quantum exact communication complexity. In particular, we consider two types of communication problems that we call promise…
Suppose Alice and Bob share a maximally entangled state of any finite dimension and each perform two-outcome measurements on the respective part of the state. It is known, due to the recent result of Regev and Toner, that if a classical…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
A central question in classical information theory is that of source compression, which is the task where Alice receives a sample from a known probability distribution and needs to transmit it to the receiver Bob with small error. This…
Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as…
In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications…
Based on an EPR pair of qubits and allowing asymptotically secure key distribution, a secure communication protocol is presented. Bob sends either of the EPR pair qubits to Alice. Alice receives the travel qubit. Then she can encode…
Let f subset of X x Y x Z be a relation. Let the public coin one-way communication complexity of f, with worst case error 1/3, be denoted R^{1,pub}_{1/3}(f). We show that if for computing f^k (k independent copies of f), o(k…
We study the communication complexity of truthful combinatorial auctions, and in particular the case where valuations are either subadditive or single-minded, which we denote with $\mathsf{SubAdd}\cup\mathsf{SingleM}$. We show that for…
A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$…
Wireless secret sharing is crucial to information security in the era of Internet of Things. One method is to utilize the effect of the randomness of the wireless channel in the data link layer to generate the common secret between two…
Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given…
The LogRank conjecture of Lov\'asz and Saks from 1988 is the most famous open problem in the communication complexity theory. The statement is as follows: Suppose that two players intend to compute a Boolean function $f(x,y)$ when $x$ is…