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  • Print publication year: 2009
  • Online publication date: June 2012

18 - Qubit measurements, superdense coding, and quantum teleportation

Summary

This chapter is concerned with the measure of information contained in qubits. This can be done only through quantum measurement, an operation that has no counterpart in the classical domain. I shall first describe in detail the case of single qubit measurements, which shows under which measurement conditions “classical” bits can be retrieved. Next, we consider the measurements of higher-order or n-qubits. Particular attention is given to the Einstein–Podolsky–Rosen (EPR) or Bell states, which, unlike other joint tensor states, are shown being entangled. The various single-qubit measurement outcomes from the EPR–Bell states illustrate an effect of causality in the information concerning the other qubit. We then focus on the technique of Bell measurement, which makes it possible to know which Bell state is being measured, yielding two classical bits as the outcome. The property of EPR–Bell state entanglement is exploited in the principle of quantum superdense coding, which makes it possible to transmit classical bits at twice the classical rate, namely through the generation and measurement of a single qubit. Another key application concerns quantum teleportation. It consists of the transmission of quantum states over arbitrary distances, by means of a common EPR–Bell state resource shared by the two channel ends. While quantum teleportation of a qubit is instantaneous, owing to the effect of quantum-state collapse, it is shown that its completion does require the communication of two classical bits, which is itself limited by the speed of light.

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Gottesman, D. and Chuang, I. L., Quantum teleportation is a universal computational primitive. Nature, 402 (1999), 390–3
Huang, Y.-F., Ren, X.-F., Zhang, Y.-S., Duan, L.-M., and Guo, G.-C., Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Letts., 93 (2004)