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Questions tagged [projection-operator]

A projection operator is one which when acts upon a quantum state (which is an element of a Hilbert space), "projects" it onto a subspace or onto another element of the same Hilbert space.

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Confusion about the relation between POVMs and projective measurements

I'm a little confused about the terminology of measurement. So say that we have the single qubit state $|\phi \rangle=c_0|0\rangle+c_1|1\rangle$. If we perform the projective measurement $P_0=|0\...
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Projecting $\lvert ++ \rangle$ on Bell Basis

I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because, $$ CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...
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Quantum channel representation of projective measurement

Let $P$ be a projector and $Q = I-P$ be its complement. How to find probability $p$ and unitaries $U_1, U_2$ such that for any $\rho$, $P\rho P + Q\rho Q = p U_1\rho U_1^\dagger + (1-p)U_2\rho U_2^\...
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Weeding out qubit states with leftmost qubit as 1

Need help! I was working on a project when I required to use a projection operator. For an example case, I have the Bell state, $$|\psi\rangle = \frac1{\sqrt2}\left(\color{blue}{|0}0\rangle+|11\rangle\...
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Error syndromes and recovery procedure in bit flip code

This question relates to exercise 10.4 in Nielsen and Chuang. For syndrome diagnosis, the textbook provides an example where one has four projectors, by which, you can identify where a one qubit ...
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1answer
60 views

What does it mean to perform a measurement in correspondence with different projections?

In error correction, like the bit flip, you perform a measurement which corresponds to different projections so that the outcomes can teach you about the error. What does it mean? How do you actually ...
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1answer
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Projection operators and positive operators

I recently came across the concepts of operators. However with current my knowledge I am unable to solve the following problem.Given an operator $$\vec{A}=\frac{1}{2}(I+\vec{n}.\vec{\sigma})$$ where $\...
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110 views

Confusion regarding projection operator

Suppose we have a qutrit with the state vector $|\psi\rangle = a_0|0\rangle + a_1|1\rangle + a_2|2\rangle$, and we want to project its state onto the subspace having the basis $\{|0\rangle,|2\rangle\}$...