Recent content by Morbert

Yes, and as @gentzen mentioned: A projector that is of rank > 1 cannot by itself be a state, mixed or pure. If a state is a projector it must be rank 1, and hence pure.

Yeah. I wasn't sure if the "i.e." was pertaining to "density operator" or to "projector"

Yes, with the caveat about your "i.e." A projector does not have to be rank 1, and hence does not have to be associated with a vector in Hilbert space. A mixed state can be a weighted sum of projectors of varying ranks, but a pure state is a projector of rank 1.

I find this review helpful https://www.kevinaylward.co.uk/qm/eis.pdf These are the broad patterns of the usage of words I have observed. Statistical: Quantum mechanics asserts statistical properties Ensemble: Quantum states represent infinite ensembles of identically prepared systems Minimal...

From the message I linked Both pure and mixed states are density operators/matrices. A density operator that is a projector onto a subspace of dimensionality 1 (and hence associated with an element ##\psi## of Hilbert space) is a pure state.

For posterity: An old thread post discussing some general subtleties that might eventually be relevant here https://www.physicsforums.com/threads/is-the-quantum-classical-boundary-the-most-important-question-in-physics.979192/post-6252131

Mixed states have nonzero von Neumann entropy, and e.g. a pure state ##|\psi\rangle\langle\psi|## where ##|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)## will not give the same expectations and variances for all observables as a mixed state ##\frac{1}{2}(|0\rangle\langle0| +...

I don't think I understand this claim. By probability set, are you referring to a probability measure? What does it mean to have a sample space for contrafactual measurements? Given a classical system and classical theory, the sample spaces of two different measurement procedures are always...

The quote by Lock is a stronger statement than what the paper argues, so I find the quote strange. The paper argues that a typical account of measurement relies on a time-controlled application of a von-Neumann-type Hamiltonian to obtain a state with a spectrum broadcast structure (SBS), when...

@Leandro Bolonini An example paper exploring possible relations between primordial fluctuations and large-scale structures: https://arxiv.org/abs/2207.06317

Von Neumann, in chapter VI, discusses psycho-physical parallelism -- "that it must be possible so to describe the extra-physical process of the subjective perception as if it were in reality in the physical world" -- as a fundamental requirement of the scientific viewpoint. He says the content...

The bit in bold is not true. Neither Wigner's nor von Neumann's accounts say or imply this.

Standard quantum theory says any coincident signal/idler detection events that resolve which way information will not produce an interference pattern. This is not contradicted by the conscious observer/material divide of Wigner or the observer/system divide of von Neumann. No. The only way to...

Standard quantum theory is used to compute the likelihood of outcomes of experimental tests. It does not commit you to a particular understanding of the language of the theory, so long as experiments are modeled appropriately. In the simple case where the orthogonal polarizers are in place...

Standard quantum theory will correctly predict the pattern produced on the back screen over many experimental runs, no matter the experimental setup, and the language of standard quantum theory can be consistently framed in terms of a conscious/material divide in line with literature by Wigner...