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The density operator describes a quantum system in a (in general mixed) state.

2 votes
2 answers
197 views

Why is this the right form for the density operator in "classical" mixture cases?

It is well known that the set of density operators $\{\rho\}$ for a quantum theory form a convex set. As I have seen them defined, we simply say that a state corresponds to some linear operator $\rho$ …
EE18's user avatar
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3 votes
0 answers
118 views

Can a mixed state be a stationary state?

If we define a stationary state as a state in which the probability distributions for every observable are constant in time, is it fair to say that a mixed state can also be a stationary state? One us …
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2 votes
2 answers
147 views

Mixed-State Density Matrices Versus Physical Ensembles

I am trying to follow a discussion (distinguishing the two sorts of systems mentioned in the title of this question) in Schlossahuer's book, Decoherence: And the Quantum-To-Classical Transition. Schlo …
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2 votes
1 answer
147 views

Does an entangled composite system necessarily imply a nonpure reduced density matrix for a ...

This question is motivated by understanding decoherence processes. Consider a bipartite quantum system $S$ composed of two subsystems, $S_{soi}$ (soi = system of interest) and $S_{env}$ (env = environ …
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0 votes
1 answer
117 views

A general theorem about state operators as a convex set?

I am trying to convince myself of a general theorem which fully "defines" the set of state operators. It is easy to prove that any convex combination of valid state operators is also a valid state ope …
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0 votes
0 answers
46 views

Collapse postulate in the density operator formalism [duplicate]

To the extent that the collapse postulate holds, textbooks will almost invariably restrict the discussion to contexts in which states are represented by normalized kets, so that the collapse postulate …
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2 votes
0 answers
145 views

Showing there are infinitely many decompositions of a non-pure state [duplicate]

Consider Problem 2.10 from Ballentine (paraphrased): Show (by constructing an example depending on a continuous parameter) that this can be done in infinitely many ways. I'm not sure how to proceed. …
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2 votes
1 answer
184 views

What is the most general mathematical structure for representing a state in QM?

In quantum mechanics textbooks which are a little more careful it is common to see it noted that a (pure) quantum state is not a vector $|\psi\rangle$ but rather a ray in Hilbert space, $c|\psi\rangle …
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1 vote
1 answer
83 views

If a state operator factors, then it factors into partial state operators in particular -- why?

Suppose that we have a state operator for a bipartite quantum system $\rho = A \otimes B$. As far as I know, one must then have in particular $\rho^{(1)} = A$; that is, if a state operator factors the …
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6 votes
6 answers
441 views

On state transformations and the requirement of space-time invariance in (non-relativistic) ...

I am trying to follow the development in Ballentine's Quantum Mechanics: A Modern Development but am struggling a lot. Please excuse my attaching of a picture of the development, but my question quite …
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4 votes
1 answer
248 views

Is a state being unentangled equivalent to statistical independence for all pairs of subsyst...

I imagine the answer is yes since, if so, the definition of unentangled is rather non-obvious and yet it gives an operational way to check for statistical independence. I am working with the standard …
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