User user1936752

18 votes

2 answers

444 views

Can we combine the square roots inside the definition of the fidelity?

fidelity information-theory

tparker

2,107

asked Feb 18, 2020 at 2:10

13 votes

1 answer

408 views

What are min and max overlaps of a maximally entangled state with a separable state?

Jules

133

asked Aug 23, 2021 at 4:45

10 votes

4 answers

640 views

How is quantum teleportation generalized to qudits?

teleportation qudit

user820789

3,202

asked Dec 17, 2018 at 22:40

8 votes

1 answer

1k views

How does the vectorization map relate to the Choi and Kraus representations of a channel?

quantum-operation kraus-representation

Tobias Fritzn

591

asked Mar 29, 2019 at 17:19

7 votes

1 answer

133 views

Positive semidefinite relationship after partial trace

quantum-operation partial-trace

JRT

395

asked Dec 15, 2020 at 17:47

7 votes

0 answers

107 views

How large can we make the fidelity between mixed states by allowing unitaries?

quantum-state unitarity fidelity

JRT

395

asked Sep 21, 2021 at 9:16

6 votes

2 answers

2k views

Partial trace over a product of matrices - one factor is in tensor product form

density-matrix nielsen-and-chuang information-theory tensor-product partial-trace

Mahathi Vempati

1,526

asked Dec 25, 2018 at 8:15

6 votes

2 answers

65 views

If $\rho,\sigma$ are classical-quantum states, can the fidelity $F(\rho,\sigma)$ be expressed in terms of $F(\rho_i,\sigma_i)$?

quantum-state fidelity trace-distance

Wut

63

asked Jun 15, 2021 at 11:21

5 votes

1 answer

57 views

If $\text{supp}(\rho_{AB})\subset \text{supp}(\sigma_{AB})$, is $\text{supp}(\rho_{A})\subset \text{supp}(\sigma_{A})$?

quantum-state partial-trace

lolwut

53

asked Mar 8, 2021 at 10:56

5 votes

1 answer

122 views

Is the quantum min-relative entropy $D_{\min}(\rho\|\sigma)=-\log(F(\rho, \sigma)^2)$ or $D_{\min}(\rho\|\sigma)=-\log(tr(\Pi_\rho\sigma))$?

information-theory entropy fidelity relative-entropy min-entropy

James

51

asked Jul 16, 2020 at 23:07

5 votes

2 answers

135 views

Can every bipartite state be written as $\rho_{AB} = \sum_{ij} c_{ij}\sigma_A^i\otimes \omega_B^j$?

quantum-state tensor-product

Alice Munroe

53

asked Oct 20, 2020 at 0:21

5 votes

2 answers

103 views

Prove that $\rho_{AB} \leq |B|(\rho_A\otimes I_B)$ for any bipartite state $\rho_{AB}$

quantum-state linear-algebra partial-trace

polp

51

asked Jan 3 at 8:50

4 votes

1 answer

285 views

Eigenvalues of a quantum state after partial tracing

quantum-state mathematics partial-trace

Heather

41

asked Sep 22, 2020 at 19:56

4 votes

1 answer

29 views

Does $\frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}=\rho_{AB}$ hold for a state $\rho_{AB}$ and projector $\Pi_A$?

quantum-state textbook-and-exercises partial-trace projection-operator

Jonah

43

asked Feb 23, 2021 at 7:16

3 votes

2 answers

1k views

What is the "complementary map" of a channel with given Kraus decomposition?

quantum-operation kraus-representation

Tobias Fritzn

591

asked Mar 28, 2019 at 8:49

3 votes

0 answers

40 views

Permutation invariant states have permutation invariant purifications - proof?

quantum-state partial-trace

JRT

395

asked Jun 2, 2021 at 8:34

3 votes

2 answers

118 views

Can we express $\mathrm{tr}_A((A\otimes B)\rho_{AB})$ in terms of $A$, $B$, $\rho_A$ and $\rho_B$?

mathematics tensor-product partial-trace linear-algebra

JRT

395

asked Mar 16, 2021 at 4:39

2 votes

1 answer

70 views

How is a classical bipartite state written in quantum notation?

quantum-state density-matrix notation

AlexanderHamilton

23

asked Jul 27, 2021 at 11:20

2 votes

2 answers

273 views

How to prove generalized Uhlmann's theorem?

nielsen-and-chuang fidelity

MaudPieTheRocktorate

231

asked Jun 2, 2021 at 1:30

1 vote

1 answer

34 views

How to take the limits of the sandwiched Renyi divergences?

mathematics information-theory relative-entropy renyi-entropies

Horatio

11

asked Sep 20, 2021 at 10:31

1 vote

1 answer

52 views

Can one define a Choi state for a a classical channel?

quantum-operation information-theory

EVMaverick

13

asked Apr 9 at 15:39

Stack Exchange Network

current community

your communities

more stack exchange communities

21 Bookmarks

Can we combine the square roots inside the definition of the fidelity?

What are min and max overlaps of a maximally entangled state with a separable state?

How is quantum teleportation generalized to qudits?

How does the vectorization map relate to the Choi and Kraus representations of a channel?

Positive semidefinite relationship after partial trace

How large can we make the fidelity between mixed states by allowing unitaries?

Partial trace over a product of matrices - one factor is in tensor product form

If $\rho,\sigma$ are classical-quantum states, can the fidelity $F(\rho,\sigma)$ be expressed in terms of $F(\rho_i,\sigma_i)$?

If $\text{supp}(\rho_{AB})\subset \text{supp}(\sigma_{AB})$, is $\text{supp}(\rho_{A})\subset \text{supp}(\sigma_{A})$?

Is the quantum min-relative entropy $D_{\min}(\rho\|\sigma)=-\log(F(\rho, \sigma)^2)$ or $D_{\min}(\rho\|\sigma)=-\log(tr(\Pi_\rho\sigma))$?

Can every bipartite state be written as $\rho_{AB} = \sum_{ij} c_{ij}\sigma_A^i\otimes \omega_B^j$?

Prove that $\rho_{AB} \leq |B|(\rho_A\otimes I_B)$ for any bipartite state $\rho_{AB}$

Eigenvalues of a quantum state after partial tracing

Does $\frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}=\rho_{AB}$ hold for a state $\rho_{AB}$ and projector $\Pi_A$?

What is the "complementary map" of a channel with given Kraus decomposition?

Permutation invariant states have permutation invariant purifications - proof?

Can we express $\mathrm{tr}_A((A\otimes B)\rho_{AB})$ in terms of $A$, $B$, $\rho_A$ and $\rho_B$?

How is a classical bipartite state written in quantum notation?

How to prove generalized Uhlmann's theorem?

How to take the limits of the sandwiched Renyi divergences?

Can one define a Choi state for a a classical channel?