Quantum cryptography and quantum memory
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Abstract
In quantum key distribution (QKD), Alice selects a sequence of characters from a finite alphabet and transmits the corresponding signals, each described by a quantum state, to Bob. Between Alice and Bob, Eve---with her own receiver and transmitter---can eavesdrop. Eve is assumed to know beforehand all the possible states from among which Alice chooses. The central question is: Can Eve gain significant information about the key without influencing what Bob receives in ways that Alice and Bob can detect? This formulation implies that many options are available to Eve. It is the purpose here to discuss one of these options, where extensive use is made of the Schrodinger equation with spatial variables. This procedure of Eve---which consists of letting the quantum state of Alice scatter from a quantum memory and then, using the information thus obtained, sending a suitably chosen quantum state to Bob---is discussed in detail. Furthermore, there are ways for Alice to defeat this procedure by an unusual choice of her quantum states. This counter-measure is also presented and discussed.