The bloch vector for N-level systems

Journal of the Physical Society of Japan

Volumn 72, Issue SUPPL.C, 2003, Pages 185-188

  Kimura, Gen ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

Bloch vector coherence vector; Quantum state

Indexed keywords

EID: 33747621729     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.1143/JPSJS.72SC.185     Document Type: Conference Paper

References (21)

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14. Suppose that (i) p̂ ≥ 0, i.e., ∀χ)ε HN, (χρ̂|χ)≥0. Then, ρ̂† = ρ̂ which can be shown by using the polarization identity for ρ̂†(i-2) ρi ≥ 0 because of ρi = (ρi|ρ\ρi)≥ 0in which |ρi) is the corresponding eigenstate. Conversely, suppose that and (i-2) hold, then |χ)εHN, (χ|ρ|χ)≥ 0 which can be easily checked by expanding |χ) = ∑iχi|ρi).
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16. For a simple proof of the Newton's formulas, it is convenient to make use of a function f (t) = π =i(1 - txi) = ∑Nj-0(-1)jajtj (t ε ℝ). By differentiating this with respect to t,we obtain df(t)/dt = ∑i=1N j(-1)jajtj - On the other hand, t holds that [df (t)/dt]/f(t)= d log f (t)/dt = σsum;ni=1n/(txi-1 Compare the coefficients of t between them, one can obtain the Newton's formula.
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