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# Quantum Computing : Recent Questions and Answers

## How does one go about constructing a mixed entangled state?

In general, an entangled state is one which cannot be decomposed as $sum_{i}p_{i} bigl(rho_{i}^Aotimesrho_{i}^Bbigr)$. But such an entangled state could still be mixed in principle. How would one create...

## Prove that $Apreceq B$ implies $A=Psi(B)$ for some channel $Psi$

Define $newcommand{PP}{mathbb{P}}newcommand{ket}{lvert #1rangle}newcommand{tr}{operatorname{tr}}newcommand{ketbra}{lvert #1rangle!langle #1rvert}PP_psiequivketbrapsi$, and let $ketpsi,ketphi$ be two bipartite states such that $tr_2(PP_psi)prectr_2(PP_phi)$.Here, $Aprec B$ with $A,B$ positive operators means that the...

## Why do quantum operations need to be reversible?

Why do quantum operations need to be reversible? Is it because of the physical implementation of the qubits or operators neesd to be unitary so that the resultant states fit...

## How to get the relative phase of an entangled pair of qubits

I have an extension to the following question: How to get the relative phase of a qubit?How do I get the relative phase of a pair of entangled...

## Is there a tool to get the quantum circuit corresponding to a sparse matrix?

If I know a sparse matrix, is there any tool that allows me to get the corresponding quantum circuit directly? If not what should I do? For example，I want to...