All Questions
Tagged with mathematical-physics density-operator
16
questions
4
votes
1
answer
126
views
Jensen's inequality on (super)operator exponential
Let us define the expectation value $\langle A\rangle_{\rho}$ of a superoperator $A$ over a density matrix $\rho$ as $(\rho, A(\rho))$, where the scalar product between operators reads $(O_1,O_2):= Tr[...
- 325
1
vote
0
answers
47
views
Why does the finite trace of density matrix imply a discrete Schmidt decomposition? [closed]
In the paper defining an average Schmidt number for a particular entangled system, Law and Eberly say:
Because density matrices always have finite trace, the Schmidt decomposition is always discrete, ...
- 9,428
6
votes
2
answers
678
views
In what sense is the set of density matrices compact in infinite dimensions?
Consider a complex, infinite-dimensional and separable Hilbert space $H$ and let $\mathcal I(H)$ denote the space of trace-class operators. The set of density operators $$\mathcal S(H):= \{\rho\in \...
- 8,094
5
votes
1
answer
435
views
Is the set of density matrices on a $d$-dimensional Hilbert space compact?
The set of the density matrices is a set with elements $\rho$ satisfying the following two conditions: $0\preceq \rho $ and $\mathrm{tr}\left( \rho \right) =1$. I wonder whether the set is compact?
- 307
4
votes
2
answers
714
views
Mathematical definition of states in Quantum Theory
I was reading Valter Moretti's book on Spectral Theory and Quantum Mechanics, and saw 2 definitions of a quantum state:
1.Let $\mathcal{H}$ be a Hilbert space. A positive, trace-class linear map $\rho:...
- 689
2
votes
1
answer
89
views
Is the following map linear over the space of density matrices?
I have a map $\mathcal{N}$ from the space of two-qubit subnormalised density matrices $\mathcal{S}(\mathcal{H}_2 \otimes \mathcal{H}_2)$ to itself (positive operators with trace between 0 and 1). ...
- 25
2
votes
1
answer
221
views
On the definition of the bosonic one-particle reduced density matrix
Consider the bosonic/fermionic Fock space $F^\pm:=\bigoplus\limits_{N=0}^\infty H_N^{\pm}$, where $H^+_N:=\vee^N \mathfrak h$ and $H^-_N:=\wedge^N \mathfrak h$ for some (complex, separable) one-...
- 8,094
2
votes
0
answers
89
views
In what way is conditional quantum probability restrictive, and why?
This is close to a duplicate of https://mathoverflow.net/q/412327/ but with a different emphasis. Unlike the mathoverflow equivalent, here I want to ask for your informed intuition as physicists.
To ...
- 121
7
votes
0
answers
1k
views
What is density matrix in QFT?
In quantum mechanics exist fundamental object Density matrix. (See for introduction last chapter in Principles of Quantum Mechanics by David Skinner). Density matrix nesesary to describe systems
even ...
- 5,707
3
votes
1
answer
441
views
Post-measurement density matrix derivation
This is something standard, by I'm trying to redo this with spectral theory. Suppose we start with the usual postulates of quantum mechanics:
States are unit rays on a separable Hilbert space. In ...
- 36.4k
2
votes
0
answers
57
views
The role of $\dim H_n$ in the definition of asymptotically continous functions on vectors
When considering the asymptotic continuity of quantum states, one works with asymptoticallycontinuous functions.
In the definition one has the following, a funtion $f$ is asymptotically cts if for a ...
- 89
0
votes
1
answer
207
views
Can one test an octonionic interpretation for a quantum-information conjecture, apparently valid in the real, complex and quaternionic settings?
For the values $\alpha = \frac{1}{2},1, 2$, corresponding to real, complex and quaternionic scenarios, the formulas (https://arxiv.org/abs/1301.6617, eqs. (1)-(3))
\begin{equation} \label{Hou1}
P_1(\...
- 165
2
votes
3
answers
673
views
Expression of density operator
States in Quantum Mechanics can be thought of as density operators, i.e., positive semi-definite, normalized trace class operators on a Hilbert Space $\mathcal{H}$.
In the case $\mathcal{H}=\mathbb{C}^...
- 313
3
votes
1
answer
647
views
Prove the solution of von Neumann equation will never stabilize if Hamiltonian and initial density matrix commutes
Given von Neumann equation
$$\frac{d}{dt} \rho(t) = -i [H, \rho(t)] = -i e^{-iHt}[H, \rho(0)]e^{iHt}.$$
If we know that $[H, \rho(0)] \neq 0$, how do we prove in details the solution of von Neumann ...
- 335
6
votes
1
answer
739
views
Hilbert space for Density Operators (instead of Banach spaces)
Is it possible to construct a well defined inner-product (and therefore orthonormality) within the set of self-adjoint trace-class linear operators? In the affirmative case, dynamics could be analyzed ...
