All Questions
Tagged with textbook-and-exercises probability
17
questions
4
votes
1
answer
68
views
Bound on success Probability for Regev's factoring algorithm
Theorem 4.1 in Regev's paper talks about a theorem due to Pomerance as follows:
Theorem 4.1: Suppose G is a finite abelian group with minimal number of generators $r$. Then, when choosing elements ...
- 711
1
vote
0
answers
68
views
How does Chernoff's bound help to solve Exercise 6.4.2 in Kaye et al.'s textbook? [duplicate]
I was wondering if anyone could help me with this question, I'm kind of new to quantum computing in general. I understand the Deutsch Josza Algorithm, but I'm not really sure where to even begin with ...
- 19
0
votes
1
answer
45
views
Calculate of theoretical probabilities for the outcomes
I have a $|+\rangle$ state qubit and I measure it in a random basis. The random basis is made with random $\theta$, $\varphi$ and $\lambda$ of $U3$ gate. How can I calculate the theoretical ...
- 9
3
votes
2
answers
123
views
How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
- 57
1
vote
1
answer
158
views
How to calculate probability of measuring $|1\rangle$ after application of $R_x$ gate
I was trying to understand how to calculate
the probability of measuring $|1\rangle$ when executing the following circuit in Qiskit:
...
- 145
1
vote
2
answers
100
views
Confusion on the probability of measuring first qubit of a separable mixed state
Let $\rho = \sum_{x \in \{0,1\}^n} P_x |x \rangle\langle x|$ be a separable mixed state over bit strings $x$ of size $n$. Suppose also that $U = U_1 \otimes \cdots \otimes U_n$ is a product of local ...
- 499
1
vote
1
answer
546
views
How do you find the possible measurement values of an observable?
$\newcommand{\ket}[1]{\left|#1\right>}$
Note: I considered posting this as an update to a prior question, but it seemed like it should be it's own post.
So this is a very basic question, but one I'...
-1
votes
1
answer
108
views
Why is $|P_0- P_1|=1$?
I have a question
we have $ |0 \rangle, |1 \rangle, |+ \rangle$ and $|- \rangle, $ defined as usual.
Let $P_0$= probability that a state be in 0, $P_+$= probability that a state be in +, and same ...
- 309
-2
votes
1
answer
152
views
Probability outcome $0$? Post measurement state?
Does anyone know how to solve this exercise? Here is the question:
Let $|\psi\rangle$ be an arbitrary pure $n$-qubit state, i.e.
$$|\psi\rangle=\sum_{x_1,\ldots,x_n=0,1}\alpha_{x_1\cdots x_n}|x_1\...
- 9
4
votes
3
answers
509
views
How do we achieve mathematically that the probability that Eve learns $x$ is $\cos^{2}\left ( \frac{\pi }{8} \right )$?
I'm trying to understand this problem.
Alice I attempting to send a 2 classical bit message to Bob using 1 qubit such that there are 4 states $\varphi_{00}$ $\varphi_{01}$ $\varphi_{10}$ $\varphi_{11}$...
- 149
5
votes
1
answer
513
views
Can all mixed states be written as a convex combination $\rho=\sum_j p_j |\psi_j\rangle\langle \psi_j|$?
States belonging to some space $\mathcal H$ can be described by density operators $\rho\in L(\mathcal H)$ that are positive and have trace one. Pure states are the ones that can be written as $\rho=|\...
- 63
2
votes
1
answer
492
views
How to prove that the mutual information is subadditive?
Let $\mathbf x=(x_1,...,x_n)$ and $\mathbf y=(y_1,...,y_n)$ be two vectors of random variables. To make things concrete, assume that Alice sends each component $x_j$ through a noisy channel to Bob, ...
- 163
2
votes
1
answer
266
views
Measurement probability of a state from three hilbert spaces
I'm curious how to find the probability measurement of a state when one qubit is measured. For example this state:
$|\gamma\rangle = \frac{1}{\sqrt{2}}(| 010 \rangle + | 101 \rangle )$
Assuming these ...
- 287
3
votes
1
answer
1k
views
Probability of measuring one qubit from the state of two qubits
I am new to quantum information and I am trying to work on some problems but I have confused myself over a qubit problem. I have the state of two qubits $|\psi\rangle_{AB}=a_{00}|00\rangle+a_{01}|01\...
user14766
4
votes
1
answer
107
views
What's the difference between $p(i|m)$ and $p(m|i)$ in measurement?
Suppose we perform a measurement described by measurement operators $M_m$. If the initial state is $|{\psi_i}\rangle$, then the probability of getting result $m$ is
$$
\begin{align}
p(m|i)=\| M_m|\...
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