By Daniel T. Gillespie

ISBN-10: 0700222901

ISBN-13: 9780700222902

Publication by means of Gillespie, Daniel T

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Two arbitrarily chosen q-physical quantities are, however, not compatible in general. 11) of a given q-physical quantity, will always commute, they are compatible, hence they can be measured simultaneously, cf. Sect. 1, in projective measurements. Certain incompatible physical quantities can be measured in non-projective measurements. 12) are not compatible ˆ n may not commute. 1: we lose repeatability of the measurement. 13) simplify significantly for a pure state ρˆ = |ψ ψ|. The measurement outcome is still one of the eigenvalues Aλ .

53) If Aˆ is a q-physical quantity of the elementary subsystem then, in a natural way, one can introduce its arithmetic mean, over the n subsystems, as a collective q-physical quantity: Aˆ ⊗ Iˆ⊗(n−1) + Iˆ ⊗ Aˆ ⊗ Iˆ⊗(n−2) + · · · + Iˆ⊗(n−1) ⊗ Aˆ . 54) Collective q-physical quantities are not necessarily of such simple form. Their measurement is the collective q-measurement. Contrary to the classical theory, not all collective q-measurements can be reduced to independent measurements on the n subsystems, cf.

13]. 26 4 Foundations of q-physics Aˆ = ˆ= Aλ Pˆλ , B ˆµ . 30) µ λ ˆ in subsequent projecLet us measure both q-physical quantities, Aˆ first and then B, tive measurements. 16): ρˆ → ˆ µ Pˆλ ρˆPˆλ Q ˆµ Pˆλ ρˆPˆλ Q → . 31) ˆ → Bµ is the secwhere pµλ is the probability that Aˆ → Aλ is the first, then B ond measurement outcome. Obviously, if we had performed the two measurements in the reversed order then the distribution of the measurement outcomes would in ˆ are not simultageneral be different. This we interpret in such a way that Aˆ and B neously measurable.

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A quantum mechanics primer by Daniel T. Gillespie


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