Teleportation as a quantum computation

Among the many exciting new applications of quantum physics in the realm of computation and information theory, I am particularly fond of quantum cryptography, quantum computing and quantum teleportation [5]. Quantum cryptography allows for the confidential transmission of classical information under the nose of an eavesdropper, regardless of her computing power or technological sophistication [2, 1, 4]. Quantum computing allows for an exponential amount of computation to take place simultaneously in a single piece of hardware [9, 7]; of particular interest is the ability of quantum computers to factorize numbers very efficiently [14], with dramatic implications for classical cryptography [6]. Quantum teleportation allows for the transmission of quantum information to a distant location despite the impossibility of measuring or broadcasting the information to be transmitted [3]. Each of these concepts had a strong overtone of science fiction when they were first introduced. If asked to rank these ideas on a scale of technological difficulty, it is tempting to think that quantum cryptography is easiest while quantum teleportation is the most outrageous—especially when it comes to teleporting goulash [11]! This ranking is correct with respect to quantum cryptography, whose feasibility has been demonstrated by several experimental prototypes capable of reliably transmitting confidential information over distances of tens of kilometres [12, 13, 10]. The situation is less clear when it comes to comparing the technological feasibility of quantum computing with that of quantum teleportation. On the one hand, quantum teleportation can be implemented with a quantum circuit that is much simpler than that required by any nontrivial quantum computational task: the state of an arbitrary qubit (quantum bit) can be teleported with as few as two quantum exclusiveor (controlled-not) gates. Thus, quantum teleportation is significantly easier to implement than quantum computing if we are concerned only with the complexity of the required circuitry. On the other hand, quantum computing is meaningful even if it takes place very quickly—indeed its primary purpose is increased computational speed—and within a small region of space. Quite the opposite, the interest