# Tag Info

Accepted

### Bound on success Probability for Regev's factoring algorithm

This is just Markov's inequality that states that for a positive random variable $X$ and $a > 0$ then $$P( X \geq a ) \leq \frac{E(X)}{a}.$$ see the wikipedia: https://en.wikipedia.org/wiki/...
Accepted

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

Yes, you can use $\rho - \sigma$ to construct a measurement where the measurement statistics differ for $\rho$ compared to $\sigma$. The issue is that $\rho - \sigma$ is not necessarily positive, ...
• 7,253
Accepted

### 40th Question IBM Sample test

Qubits are initially in the ∣0⟩ state. The Rz gate, which is a rotation around the z-axis, only changes the phase of the qubit states and not the probabilities of measuring 0 or 1 in the computational ...
• 652
Accepted

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

TL;DR: No. As pointed out by @Tristan Nemoz in the comments, $p_x=\frac{1}{2^{n-1}(2^n+1)}$ independently of $x$, so for $n\geqslant 2$ the conjectured inequality fails. The output probabilities $p$ ...
• 23.6k
Accepted

• 26.1k
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 ...
• 60.3k
Accepted

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

I suspect you're misinterpreting the statement a little. The claim will not be that for every possible value of $T$ the probability is at least 1/8. Instead, the success probability, averaged across ...
• 60.3k
1 vote
Accepted

### How to get partial probability from measurements in qiskit?

You can use the marginal_counts() function from qiskit.result to get the marginalized counts for the bits that you want (...
1 vote

• 11
1 vote

### How to prove that the mutual information is subadditive?

Unlike entropy, mutual information can be either subadditive or superadditive. If $A$, $B$, $C$ are bits with equal probabilities and $A=B=C$, then $$I(A,B:C) = 1,\\ I(A:C) + I(B:C) = 2,$$ ...
• 11
1 vote

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

I won't give the final answer (close to it), but instead try and point you in the general direction. Initial State: The given initial state is $| \psi(t=0) \rangle = | 0 \rangle$. Pauli X Matrix: ...
• 839
1 vote
Accepted

### How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

If you consider the state $$\Omega_- = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle).\tag{1}$$ you will find that there is NO violation. Let me show this. Note that the approach I will use for solving ...
• 126
1 vote

### How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

From your current description, it seems that you have found each eigenvector $\{|v_1\rangle,...,|v_4\rangle\}$ and its associated eigenvalue $\lambda_1,...,\lambda_4$. These eigenvalues represent the ...

Only top scored, non community-wiki answers of a minimum length are eligible