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- Hartmut Klauck
- SIAM J. Comput.
- 2001

We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower bounds developed by Raz [30] to the quantum case. Applying this method we give an exponential separation between bounded… (More)

- Juraj Hromkovic, Sebastian Seibert, Juhani Karhumäki, Hartmut Klauck, Georg Schnitger
- Inf. Comput.
- 2002

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa's) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the… (More)

- Hartmut Klauck, Robert Spalek, Ronald de Wolf
- 45th Annual IEEE Symposium on Foundations of…
- 2004

A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability is exponentially small in k. We establish such theorems for the classical as well as quantum query complexity of the OR function. This implies slightly… (More)

- Rahul Jain, Hartmut Klauck
- 2010 IEEE 25th Annual Conference on Computational…
- 2010

We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the partition bound is stronger than both the rectangle/corruption bound and the γ2/generalized discrepancy bounds. In the… (More)

- Hartmut Klauck
- STOC
- 2000

We investigate the power of quantum communication protocols compared to classical probabilistic protocols. In our first result we describe a total Boolean function that has a quantum Las Vegas protocol communicating at most O(N 1°/11+~) qubits for all e > 0, while any classical prob-abilistic protocol (with bounded error) needs ~(N/log N) bits. Then we… (More)

- Hartmut Klauck
- ICALP Satellite Workshops
- 2000

This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum communication complexity.

- Hartmut Klauck
- STOC
- 2003

We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds <i>n</i>/log… (More)

- Hartmut Klauck, Ronald de Wolf
- STACS
- 2013

We use the venerable " fooling set " method to prove new lower bounds on the quantum communication complexity of various functions. Let f : X × Y → {0, 1} be a Boolean function, fool 1 (f) its maximal fooling set size among 1-inputs, Q * 1 (f) its one-sided-error quantum communication complexity with prior entanglement, and N Q(f) its nondeterministic… (More)

- Hartmut Klauck
- STOC
- 2010

A strong direct product theorem states that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then the overall success probability will be exponentially small in k. We establish such a theorem for the randomized communication complexity of the Disjointness problem, i.e., with… (More)

- Hartmut Klauck, Ashwin Nayak, Amnon Ta-Shma, David Zuckerman
- STOC
- 2001

One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with exponentially fewer qubits than possible classically [3, 26]. Moreover, these methods have a very simple… (More)