Add to ORKGWe extend Shi's 2002 quantum lower bound for collision in $r$-to-one functions with $n$ inputs. Shi's bound of $\Omega((n/r)^{1/3})$ is tight, but his proof applies only in the case where the range has size at least $3n/2$. We give a modified version of Shi's argument which removes this restriction
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical...
Given a random function $f$ with domain $[2^n]$ and codomain $[2^m]$, with $m \geq n$, a collision o...
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. ...
The collision problem is to decide whether a function X: {1,..., n} → {1,..., n} is one-to-one or t...
The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-o...
We prove tight Ω(n1/3) lower bounds on the quantum query complexity of the Collision and the Set Equ...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
In the classical hashing theory, collision is a coincidence of the values of a function with differe...
Abstract. In a breakthrough result, Razborov (2003) gave optimal lower bounds on the quantum communi...
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $l$...
This work proves an improved lower bound for the quantum query complexity of collision- finding in h...
AbstractWe propose a new method for proving lower bounds on quantum query algorithms. Instead of a c...
Abstract. We prove lower bounds on the bounded error quantum communication complexity. Our methods a...
We study the quantum query complexity of finding a collision for a function $f$ whose outputs are ch...
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on...
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical...
Given a random function $f$ with domain $[2^n]$ and codomain $[2^m]$, with $m \geq n$, a collision o...
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. ...
The collision problem is to decide whether a function X: {1,..., n} → {1,..., n} is one-to-one or t...
The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-o...
We prove tight Ω(n1/3) lower bounds on the quantum query complexity of the Collision and the Set Equ...
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, includ...
In the classical hashing theory, collision is a coincidence of the values of a function with differe...
Abstract. In a breakthrough result, Razborov (2003) gave optimal lower bounds on the quantum communi...
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $l$...
This work proves an improved lower bound for the quantum query complexity of collision- finding in h...
AbstractWe propose a new method for proving lower bounds on quantum query algorithms. Instead of a c...
Abstract. We prove lower bounds on the bounded error quantum communication complexity. Our methods a...
We study the quantum query complexity of finding a collision for a function $f$ whose outputs are ch...
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on...
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical...
Given a random function $f$ with domain $[2^n]$ and codomain $[2^m]$, with $m \geq n$, a collision o...
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. ...