# Questions tagged [probability]

For questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities.

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### Stabilizer States - Calculating measurement probabilities with the rank of the stabilizer table's X-block

Consider a $n$-Qubit stabilizer state $\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}\rho = \ket{\psi}\bra{\psi}$ and its $n \times 2n$ boolean stabilizer tableau. Any ...
1 vote
158 views

### 40th Question IBM Sample test

Given this code fragment, what is the probability that the measurement would result in 1? qc = QuantumCircuit(1) qc.rz(3 * math.pi/4, 0) A] 0 B] 0.14645 C] 0.85355 ...
1 vote
94 views

### Matrix representation of the symmetric subspace for two copies

Consider two copies of an $n$ qubit Haar random state, given by: \rho = \mathbb{E}_{U \sim \mathsf{Haar}}\left[U |0^n\rangle \langle 0^n| U^{*}\otimes U |0^n\rangle \langle 0^n| U^{*}\...
66 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 ...
51 views

### Existence of a two-outcome measurement $M$ such that the induced distributions differs between different density matrices

Let $\rho \neq \sigma$ be density matrices. I want to show that there exists a two-outcome measurement $M$ such that the induced distributions $M(\rho)$ and $M(\sigma)$ differ. From what I learned, ...
57 views

### How to compute the measurement probability in the Hadamard test?

In the Hadamard test (e.g., page 40 of these lecture notes) we have: But if you look at standard textbook reference, like Nielsen and Chuang, there's an example for how to compute the measurement ...
1 vote
67 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 ...
84 views

### Uncertainty of estimates computed by stim/sinter

The sinter.plot_error_rate function handles the plotting of the error rates sampled by sinter. Along with the estimated error rates, it highlights a region within ...
54 views

### Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: How can I calculate the measuring probabilities of a two qubit state along a certain axis? From here I know how to calculate the probability of measuring a general state ...
24 views

1 vote
75 views

### Semi-Definite Program to maximise $P(X)$ with a fixed CHSH value

This question should be theoretically simple, yet I'm struggling as something may be incorrect about my code. I am trying to plot a graph of the maximum probability ($P(x)$) of a given system against ...
44 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 ...
47 views

### quantum generalisation of random variables

What is the quantum information equivalent of a classical probability random variable ? Is it a density matrix or an observable ? If so can someone show me how to write a random variable that follows ...
77 views

### Is there a general method for calculating expectation values for time-dependent wavefunctions?

Is there a general method for calculating expectation value? I have a workshop question, and I'm sure what a good process to follow is. It is given that $$|\psi(t = 0)\rangle = |0\rangle\,,\tag{1}$$ ...
38 views

### Kolmogorov dilations of positive definite kernels and Donsker's Delta

I'm having problems understanding a part of the proof of Kolmogorov’s dilation theorem (Theorem 3.2 given in this). We define a map $V_K:S\to H$ given by $V_K(x):=\delta_x+N$. Then, we compute the ...
122 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 ...
110 views

### Minimum probability of measuring marked state in Grover's algorithm is 1/8

I recently came across the proposition that for a database containing $N$ elements with $m<\sqrt{N}$ marked elements, applying Grover's algorithm with any $T$ $(0<T<\sqrt{N}-1)$ iterations (...
115 views

### How to compute marginal probabilities of Alice's qubit (in density operator language)?

Let $| \psi \rangle = \frac{1}{\sqrt{2}}|00\rangle + \frac{1}{2}|01\rangle + \frac{\sqrt{3}}{4} |10\rangle + \frac{1}{4}|11\rangle$ be a state vector describing a closed quantum mechanical system. ...
138 views

### Density matrix and State vector give different result in mesolve in QuTiP

qutip mesolve gives me different population evolve depending on that initial state is state vector or density matrix. And, in some situation, it gives me negative population. It doesn't make sense... ...
146 views

### Given averages of powers of position and momentum in quantum mechanics what information can be secured about the wave-function?

Question If I tell you all the averages of powers of position and momentum in quantum mechanics can you tell me the value of the wave-function? What can you tell me about the wavefunction? Is there ...
1 vote
51 views

### Saturating an inequality relating the operator norm and the total variation distance

Let $U$ be an $n$-qubit unitary, and let $p_U(x) = |\langle x | U | 0\rangle |^2$ be the probability of obtaining $x \in \{0,1\}^n$ on the all zero input. Given two $n$-qubit unitaries $U$ and $V$, it ...
### Given a unitary $U_p:|0\rangle\to\sum_\omega\sqrt{P(\omega)}|\omega\rangle$, what does $|0\rangle$ represent exactly?
Consider a random variable $X$ on a probability space $(\Omega, 2^\Omega, P)$. Let $H_\Omega$ be a Hilbert space with basis states ${| \omega \rangle}_{\omega \in \Omega}$, and fix a unitary $U_P$ ...