This is for the Pauli Matrics 0 and 1 are different Hilbert Spaces(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left[(I-Z)_{0}\otimes(I-Z)_{1} , Y_{0}\otimes Z_{1}\right][/tex]

[tex]=\left((I-Z)_{0}\otimes(I-Z)_{1}\right)\left(Y_{0}\otimes Z_{1}\right)-\left(Y_{0}\otimes Z_{1}\right)\left((I-Z)_{0}\otimes(I-Z)_{1}\right) [/tex]

[tex]=\left((I-Z)_{0}Y_{0}\otimes(I-Z)_{1} Z_{1} - Y_{0}(I-Z)_{0} \otimes Z_{1}(I-Z)_{1} [/tex]

[tex]= (Y_{0} -Z_{0}Y_{0}) \otimes (Z-I)_{1} - ((Y_{0} + Y_{0}Z_{0})\otimes (Z-I)_{1} [/tex]

[tex]= (Y_{0} -Z_{0}Y_{0}) \otimes (Z-I)_{1} - ((Y_{0} - Z_{0}Y_{0})\otimes (Z-I)_{1}

=0

[/tex]

I think this is wrong because I have done it long hand (i.e multiplying the matrices) and also I really, really don't want zero for an answer :).

Thanks

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# Homework Help: Commutator, where have I gone wrong?

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