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Shor, P.W. (1994) Algorithms for Quantum Computation: Discrete Log and Factoring. Foundations of Computer Science, 1994, 124-134. http://www.computer.org/csdl/proceedings/focs/1994/6580/00/0365700-abs.html

has been cited by the following article:

• TITLE: Virtual Numbers to Represent Entangled Quantum States

  AUTHORS: Lalit A. Patel

  KEYWORDS: Quantum Mechanics; Probability Amplitude; Complex Number; Entanglement; Bell State

  JOURNAL NAME: Journal of Quantum Information Science, Vol.4 No.1, February 17, 2014

  ABSTRACT: In the existing formalism of quantum states, probability amplitudes of quantum states are complex numbers. A composition of entangled quantum states, such as a Bell state, cannot be decomposed into its constituent quantum states, implying that quantum states lose their identities when they get entangled. This is contrary to the observation that a composition of entangled quantum states decays back to its constituent quantum states. To eliminate this discrepancy, this paper introduces a new type of numbers, called virtual numbers, which produce zero upon multiplication with complex numbers. In the proposed formalism of quantum states, probability amplitudes of quantum states are general numbers made of complex and virtual numbers. A composition of entangled quantum states, such as a Bell state, can then be decomposed into its constituent quantum states, implying that quantum states retain their identities when they get entangled.