I'm reading a seminal paper by Zurek on decoherence (preprint http://arxiv.org/abs/quant-ph/0105127" [Broken]), and am afraid I don't grasp one of the claims he makes. Briefly, consider an entagled state of two qubits:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|\psi{\rangle} = \sum_i x_i |A_i{\rangle}|B_i{\rangle}[/tex]

He claims that one can choose a different basis for the first qubit, and get a different representation for psi:

[tex]|\psi{\rangle} = \sum_i y_i |A'_i{\rangle}|B'_i{\rangle}[/tex]

However, if psi becomes entangled with a _third_ qubit:

[tex]|\psi{\rangle} = \sum_i x_i |A_i{\rangle}|B_i{\rangle}|C_i{\rangle}[/tex]

Then the basis ambiguity is lost: one cannot, in general, pick a different basis for A and expect to get a similar representation with alternate bases for B and C.

Perhaps my lin alg is a bit rusty, but I don't follow either claim. Can anyone elucidate?

Thanks!

[edited to use tex]

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# Basis ambiguity?

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