2 votes
Accepted

Measuring one register of the state $\frac{1}{2^{m}} \sum_{x}\sum_{k} (-1) ^ {x\cdot k} |k\rangle |f(x)\rangle$

Your state before measurement is $$ |\psi\rangle=\frac{1}{2^m}|0\rangle\sum_x|f(x)\rangle+\frac{1}{2^m}\sum_x\sum_{k\neq 0}(-1)^{x\cdot k}|k\rangle|f(x)\rangle. $$ How do we calculate the probability ...
DaftWullie's user avatar
  • 56.8k
2 votes

Why does measuring a GHZ state in the computational basis destroy the entanglement?

The two-qubit GHZ state (Bell state) case is special: any measurement in a basis $$ \cos\theta X+\sin\theta Z $$ will return perfectly correlated results between the two parties. In the case of a ...
DaftWullie's user avatar
  • 56.8k
1 vote

Getting a numeric result from the variational quantum eigensolver

Each measurement bitstring corresponds to an eigenvalue of the observable you're measuring. The output of VQE is an estimate of the expectation of the observable given by the average of these ...
Cody Wang's user avatar
  • 1,138
1 vote
Accepted

What is the explicit action of the following circuit?

I am assuming the two control symbols connecting |𝜓⟩ and |+⟩ are entangling the states somehow? Yes, this represents a CZ gate. Then I don't understand the top right measurement. It is not in a ...
Peter-Jan's user avatar
  • 1,249
1 vote

What does it mean that the elements of a generalized measurement are operators?

Forgetting for a second the way you formalise generalised measurements (that is, POVM), ask yourself how a "measurement" should be formalised in quantum mechanics. A measurement is ...
glS's user avatar
  • 23.9k
1 vote
Accepted

What does it mean that the elements of a generalized measurement are operators?

$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$ I ...
FDGod's user avatar
  • 1,739
1 vote

Performing a projective measurement, is the resulting expectation value $\langle \Psi|M|\Psi\rangle$ bounded between $+1$ and $-1$?

The measurement operators $\{M_i\}$ obey two conditions, firstly they are positive operators, $M_i\geq 0$, which is $\forall |\psi \rangle,\, \langle \psi | M_i |\psi \rangle \geq 0$. Secondly, they ...
Ethan's user avatar
  • 51

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