Communication complexity has become a central complexity model. In that model, we count the amount of communication bits needed between two parties in order to solve certain computational problems. We show that for certain communication complexity problems quantum communication protocols are exponentially faster than classical ones. More explicitly, we give an example for a communication complexity relation (or promise problem) P such that: 1. The quantum communication complexity of P is O(log m). 2. The classical probabilistic communication complexity of P is \Omega\Gamma m 1=4 = log m). (where m is the length of the inputs). This gives an exponential gap between quantum communication complexity and classical probabilistic communication complexity. Only a quadratic gap was previously known. Our problem P is of geometrical nature, and is a finite precision variation of the following problem: Player I gets as input a unit vector x 2 R n and two orthogonal subspaces M 0 ...

This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are in-terpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms

Quantum entanglement lies at the heart of new proposals for quantum communication and computation. Here we describe the recent experimental realization of quantum teleportation.

Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental

Abstract — We expand on our work on Quantum Data Hiding [1] – hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

Abstract. Mayers and independently Lo and Chau have shown that unconditionally secure quantum bit commitment is impossible. In this paper we show that under the assumption that the sender is not able to perform generalized measurements involving more than n qubits coherently (n-coherent measurements) then quantum bit commitment is possible. A commitment scheme is δ-binding if for each execution there is an ˜x ∈{0,1}that cannot be unveiled with probability of success better than δ. Our bit commitment scheme requires the transmission of N qubits and is δ-binding, for any δ>0, if the committer can only carry out n-coherent measurements for some n ∈ Ω(N). For some α> 0, the scheme is 2 −αN-binding against n-coherent measurements for some n ∈ Ω ( √ N). The security against malicious receivers is unconditional. 1

COMPUTER \Lambda

The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed. 1 Introduction and

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This paper is structured around the idea that a finite Universal Computer cannot be realized and presents in detail a series of unconventional computing paradigms supporting this idea from a quantum mechanical perspective.