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Sooraj S's user avatar
Sooraj S's user avatar
Sooraj S's user avatar
Sooraj S
  • Member for 2 years, 8 months
  • Last seen more than a week ago
7 votes
1 answer
420 views

Derivation of efficiency of Phase Estimation Algorithm

5 votes
1 answer
223 views

Cost of Modular Exponentiation in Shor's algorithm

5 votes
0 answers
372 views

Prove a circuit with controlled $iR_x(\pi \alpha)$ is universal for quantum computation whenever $\alpha$ is irrational

5 votes
2 answers
337 views

Why does the $\chi$ matrix have $d^4-d^2$ independent parameters?

4 votes
1 answer
335 views

Show that $E_k=(I\otimes\langle e_k|)U(I\otimes|e_0\rangle)$ implies $U=\begin{bmatrix}[E_1]&\cdots\\ [E_2]&\cdots\\\vdots&\ddots\end{bmatrix}$

4 votes
0 answers
353 views

Prove the equality conditions in the triangle inequality $S(A,B)\ge |S(A)-S(B)|$ for the von Neumann entropy

3 votes
0 answers
229 views

Prove $|η(r) − η(s)| ≤ η(|r − s|)$ when $|r − s| ≤ 1/2$ [closed]

3 votes
1 answer
440 views

Expansion of multi-qubit density matrix in the Pauli matrix basis

2 votes
2 answers
320 views

Derive the Concavity of Quantum Conditional Entropy from Strong subadditivity

2 votes
2 answers
205 views

How to show $T(\rho,\sigma)≥\sum_i|r_i − s_i|$ with $r_i,s_i$ eigenvalues of $\rho,\sigma$?

2 votes
1 answer
96 views

The matrix norm $\|A\|=\max_{\langle u|u\rangle=1}|\langle u|A|u\rangle|$ in the proof of Lieb's theorem

2 votes
0 answers
183 views

Prove $\beta=\Lambda\otimes\Lambda$, where $\Lambda=\dfrac{1}{2}\begin{bmatrix}I&X\\X&-I\end{bmatrix}$ for single qubit tomography

2 votes
2 answers
321 views

What is the Bloch sphere representation of $\rho\to\mathcal{E}(\rho) = |+\rangle\langle+|ρ|+\rangle\langle+| + |−\rangle\langle−|ρ|−\rangle\langle−|$?

1 vote
1 answer
135 views

Show the linearity of $(\langle a_m|\otimes I_B\otimes I_C\otimes \langle d_q|) U(I_{A}\otimes I_B\otimes |0_{C}\rangle\otimes |0_{D}\rangle)$

1 vote
1 answer
259 views

How to derive the number of independent parameters in the $\chi$ matrix from the Choi matrix?

1 vote
1 answer
86 views

Why is $\chi$ not uniquely determined by $\sum_{mn}\beta_{jk}^{mn}\chi_{mn}=\lambda_{jk}$?

1 vote
1 answer
362 views

Prove that at most $d^2$ Kraus operators are sufficient to represent any quantum operation

1 vote
1 answer
225 views

Making sense of the terms Polynomial and Exponential Precision in a Quantum Circuit

1 vote
0 answers
57 views

Probability of the case when $r'\neq r$ and $r'$ is a factor $r$ in the order finding algorithm

1 vote
1 answer
154 views

DFT like operation in the third step of Period finding and Discrete Logarithm algorithm

1 vote
1 answer
123 views

Prove that classical counting requires $k=\Omega(N)$ oracle calls

1 vote
1 answer
310 views

Hamiltonian Simulation Circuit for Grover's Search

1 vote
1 answer
998 views

Measurement of single qubit operator $U$ which is both Hermitian and unitary with eigenvalues $±1$

1 vote
0 answers
29 views

$E(U_j,V_j)\leq\Delta/(2m)$ if probabilities of outcomes obtained from the approximate circuit is within a tolerance $Δ>0$

1 vote
1 answer
180 views

Prove $E(R_n(\alpha),R_n(\theta)^n)<\epsilon/3$ from $E\big(R_n(\alpha),R_n(\alpha+\beta)\big)=|1-\exp(i\beta/2)|$

1 vote
0 answers
554 views

Circuit to show that Hadamard, phase, controlled- and Toffoli gates are universal

1 vote
2 answers
239 views

Why is dual-rail encoding called an error-detecting code for amplitude damping?

1 vote
1 answer
325 views

In what sense is $\langle\psi|\rho|\psi\rangle$ the overlap between $|\psi\rangle$ and $\rho$?

1 vote
1 answer
259 views

Conditional entropy as relative entropy between probability distributions

1 vote
1 answer
135 views

Calculation of $\frac{d}{dt} I_t(A,X)$ in proving the convexity of the relative entropy via Lieb's theorem