1
vote
1answer
39 views

A question on partial trace and density matrix computation

Consider a Pure state of a two dimensional system $|\psi\rangle={1\over\sqrt{2}}(|e_1\rangle|e_1\rangle+|e_2\rangle|e_2\rangle)$ where $\{|e_i\rangle\}$ is an orthonormal basis. Could any one just ...
4
votes
2answers
136 views

Dimension of separable state

I'm from a pure mathematics background (BSc and MSc). I’m reading Quantum Computing: From Linear Algebra to Physical Realization by Nakahara. Please can you help me to understand how the dimension ...
1
vote
2answers
163 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
191 views

Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
3
votes
1answer
63 views

Mutually unbiased bases

This question can be formulated in two ways. Let there be two $d$-dimensional orthonormal bases $B_{1}$ and $B_{2}$. I refer to the elements of $B_{1}$ by $\lvert\nu_{i}\rangle$ and to the elements of ...
3
votes
1answer
178 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
0
votes
1answer
61 views

Time evolution in a static magnetic field of a 2-level system that is actually a 3 level system

What I want to do is describe the time evolution of only two states of a spin 1 particle on the bloch sphere. However, I'm running into trouble because I don't know how to construct the hamiltonian ...
3
votes
1answer
231 views

Rotation about the $z$-axis on the Bloch sphere

I'm having some trouble with successfully working out a rotation about the $z$-axis on the Bloch sphere. Now, I know how this is performed, in principle. A rotation of the Bloch-sphere around an ...
5
votes
1answer
82 views

When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
1
vote
1answer
268 views

Proof of Pauli group preservation by Clifford group conjugation?

A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words: $C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and ...
1
vote
3answers
271 views

Anybody have example of two-qubit non-Pauli and non-Clifford quantum gate?

A lot of known quantum gates are in the Pauli group (I,X,Z,Y) or in the Clifford group (H,P,Cnot). I need examples of the quantum gates that aren't in this groups. Also, are there are matlab functions ...