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Segawa, Etsuo; Konno, Norio

Limit theorems for quantum walks driven by many coins. (English) Zbl 1165.81318

Int. J. Quantum Inf. 6, No. 6, 1231-1243 (2008).
Summary: We obtain some rigorous results on limit theorems for quantum walks driven by many coins introduced by T. A. Brun, H. A. Carteret and A. Ambainis [Phys. Rev. Lett. 91, 130602 (2003), Phys. Rev. A 67, 062317 (2003) and Phys. Rev. A 67, 032304 (2003)] in the long time limit. The results imply that whether the behavior of a particle is quantum or classical depends on the three factors: the initial qubit, the number of coins \(M, d = [t/M]\), where \(t\) is time step. Our main theorem shows that we can see a transition from classical behavior to quantum one for a class of three factors.

Cited in 12 Documents

MSC:

81P68 Quantum computation
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics

Keywords:

quantum walks; limit theorem; many coins
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\textit{E. Segawa} and \textit{N. Konno}, Int. J. Quantum Inf. 6, No. 6, 1231--1243 (2008; Zbl 1165.81318)
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