Mitchell: No, even if you want to think of the position basis as the only “real” one, how does that let you decompose any density matrix uniquely into pure states? Sure, it suggests a unique decomposition of the maximally mixed state, but how would you decompose (for example) ((1/2,1/4),(1/4,1/2))?
Mitchell: No, even if you want to think of the position basis as the only “real” one, how does that let you decompose any density matrix uniquely into pure states? Sure, it suggests a unique decomposition of the maximally mixed state, but how would you decompose (for example) ((1/2,1/4),(1/4,1/2))?