2
votes
1answer
67 views

Finding the stabilizer group given a state

Consider general pure state $|\psi\rangle$ in some hilbert space $\mathcal{H}$ (which could be a tensor product of other Hilbert spaces) I would like to know whether there is a way to ...
2
votes
0answers
31 views

How to prove that the ground state of the Hubbard model is not a Slater determinant?

Of course it is expected. But how to prove it analytically? Slater determinant is mentioned in almost every quantum mechanics textbook. But it is necessary to warn the undergraduate students that not ...
1
vote
1answer
82 views

Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
1
vote
2answers
147 views

Trace in non-orthogonal basis?

Physicists define the trace of an operator $\rho$ as the follows, $Tr(\rho)=\sum\limits_{|s\rangle \in B} \langle s| \rho |s\rangle$ where B is some orthonormal basis, and this quantity is ...
4
votes
1answer
121 views

Couder-Fort Oil Bath Experiments and Quantum Entanglement Phenomena

The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit ...
1
vote
2answers
190 views

Can we have a physical interpretation for a time independent Schrodinger equation of this form?

I am interested in a time independent Schrodinger equation of this form. $$F*\psi - \frac{\hbar^2}{2m} \frac{\partial^2{\psi}}{\partial{x^2}} = E\psi$$ Here the product $V\psi$ is replaced by the ...
1
vote
0answers
105 views

Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally recorded branches”?

I came across an unusual multi-partite generalization of the Schmidt decomposition in my work, which I describe below. Usually, when people say "a multi-partite Schmidt decomposition", they mean a ...
1
vote
3answers
242 views

Is a quantum system mandatory for generating true random sequence?

Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
3
votes
2answers
369 views

Mathematically challenging areas in Quantum information theory and quantum cryptography

I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
4
votes
2answers
368 views

Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
18
votes
1answer
344 views

Geometric picture behind quantum expanders

A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
2
votes
1answer
715 views

Simplified partial trace of two operators

If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any ...
21
votes
3answers
2k views

Why are von Neumann Algebras important in quantum physics?

At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important ...