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Results tagged with Search options user 58382
5
votes
2answers
It is well known that two-dimensional states, that is, qubits, can be represented using the Bloch sphere: all pure states lie on the surface of a three-dimensional sphere, while all the mixed states a …
asked Apr 6 '18 by glS
2
votes
1answer
Consider the quantum state fidelity $F(\rho,\sigma)$ defined as (I will use the notation used in Nielsen & Chuang here): $$ F(\rho,\sigma) \equiv \operatorname{Tr}\sqrt{\rho^{1/2}\sigma\rho^{1/2}} = \ …
asked Jun 2 '18 by glS
7
votes
2answers
Consider a separable state $\rho$ living in a tensor product space $\mathcal H\otimes\mathcal H'$, with $\mathcal H$ and $\mathcal H'$ of dimensions $D$ and $D'$, respectively. If $\rho$ is separable, …
asked Apr 13 '18 by glS
2
votes
The name of the concept you are looking for is probability amplitude. The two states $\lvert T\rangle = \frac{1}{\sqrt2}(\lvert 10\rangle + \lvert 01\rangle)$ and $\lvert S\rangle = \frac{1}{\sqrt2}( …
answered Nov 6 '16 by glS
6
votes
$\newcommand{\bs}[1]{\boldsymbol{#1}}\newcommand{\on}[1]{\operatorname{#1}}$Let $f:\mathbb R^{d^2-1}\to\mathscr B(\mathscr H)$ be the mapping from points in $\mathbb R^{d^2-1}$ to bounded operators on …
answered Aug 27 '18 by glS
2
votes
1answer
Consider a generic single-qubit state $$\rho=\lambda_1\lvert \lambda_1\rangle\!\langle \lambda_1\rvert+\lambda_2\lvert \lambda_2\rangle\!\langle \lambda_2\rvert\in\mathcal H_S.$$ I am interested in un …
asked Nov 5 '18 by glS
2
votes
It is in the sense that given any pair of states $\rho$ and $\sigma$, you have \begin{align} \operatorname{Tr}_2(\rho\otimes\sigma)&=\rho,\\ \operatorname{Tr}_1(\rho\otimes\sigma)&=\sigma. \end{align} …
answered Oct 24 '18 by glS
5
votes
A GHZ in $M=2$ would be $|00\rangle+|11\rangle$. Sure you could still call it a GHZ, but it is not very useful because this state already has a name: it's a Bell state. A standard reference to unders …
answered Apr 13 '18 by glS