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The density operator describes a quantum system in a (in general mixed) state.
2
votes
2
answers
197
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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 $\rho$ …
3
votes
0
answers
118
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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 …
2
votes
2
answers
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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 …
2
votes
1
answer
147
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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 …
0
votes
1
answer
117
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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 …
0
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0
answers
46
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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 …
2
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0
answers
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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. …
2
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1
answer
184
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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 …
1
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1
answer
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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 …
6
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6
answers
441
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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 …
4
votes
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answer
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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 …