Related papers: Lower bounds on the Deterministic and Quantum Comm…
Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that…
The question of how much communication is required between collaborating parties to compute a function of their data is of fundamental importance in the fields of theoretical computer science and information theory. In this work, the focus…
Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…
In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting…
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices…
We propose a new classical bit commitment protocol using the relativistic constraint that signals cannot travel faster than the speed of light $c$. This protocol is unconditionally secure against both classical or quantum attacks. The…
Fingerprinting is a technique in communication complexity in which two parties (Alice and Bob) with large data sets send short messages to a third party (a referee), who attempts to compute some function of the larger data sets. For the…
In this thesis, we are interested in the limits of quantum communication with and without entanglement, and with and without noise assumptions on the communication setup. When a sender and a receiver are connected by a communication line…
After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
Bound secret information is classical information that contains secrecy but from which secrecy cannot be extracted. The existence of bound secrecy has been conjectured but is currently unproven, and in this work we provide analytical and…
A transmitter Alice may wish to reliably transmit a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening…
We study the one-way two-party communication complexity of Maximum Matching in the semi-robust setting where the edges of a maximum matching are randomly partitioned between Alice and Bob, but all remaining edges of the input graph are…
We consider a communication problem in which the receiver must first detect the presence of an information packet and, if detected, decode the message carried within it. We present general nonasymptotic upper and lower bounds on the maximum…
We propose a test for certifying the dimension of a quantum system: store in it a random $n$-bit string, in either the computational or the Hadamard basis, and later check that the string can be mostly recovered. The protocol tolerates…
We consider the communication scenario where K transmitters are each connected to a common receiver with an orthogonal noiseless link. One of the transmitters has a message for the receiver, who is prohibited from learning anything in the…
In the decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), the task is to list the $k$-error occurrences of $P$ in…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…