Quantum limits to dynamical evolution

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 5, 2003, Pages 8-

  Giovannetti, Vittorio ^a   Lloyd, Seth ^a,b   Maccone, Lorenzo ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867253177     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.67.052109     Document Type: Article

References (15)

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8. V. GiovannettiS. LloydL. Macconee-print quant-ph/0303085.
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11. One is tempted to interpret the time (Formula presented) as the minimum time it takes for the system to evolve to a configuration (Formula presented) such that (Formula presented) (where the term (Formula presented) is needed for normalization purposes). However, it is possible to find counterexamples that show that this definition does not work when (Formula presented) For example, consider the mixture (Formula presented)where (Formula presented) with (Formula presented) and (Formula presented) energy eigenstates and (Formula presented) ancillary orthogonal states with null energy. This state will reach the condition (Formula presented) in a time (Formula presented) smaller than (Formula presented) if the following parameters are employed: (Formula presented)
12. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
13. Since all the (Formula presented) have zero energy ground states, then (Formula presented) for all k.
14. B. Schumacher and M. D. Westmoreland, e-print quant-ph/0004045;
15. B. SchumacherM. D. Westmorelande-print quant-ph/0112106.