User user1936752

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1 answer

53 views

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

quantum-operation information-theory

EVMaverick

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

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How is quantum teleportation generalized to qudits?

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

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How to take the limits of the sandwiched Renyi divergences?

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Horatio

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How is a classical bipartite state written in quantum notation?

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AlexanderHamilton

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asked Jul 27, 2021 at 11:20

6 votes

2 answers

68 views

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

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Wut

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asked Jun 15, 2021 at 11:21

2 votes

2 answers

293 views

How to prove generalized Uhlmann's theorem?

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MaudPieTheRocktorate

231

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3 votes

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Permutation invariant states have permutation invariant purifications - proof?

quantum-state partial-trace

JRT

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asked Jun 2, 2021 at 8:34

5 votes

1 answer

123 views

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

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James

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Positive semidefinite relationship after partial trace

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

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Mahathi Vempati

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

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JRT

395

asked Mar 16, 2021 at 4:39

5 votes

1 answer

58 views

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

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lolwut

53

asked Mar 8, 2021 at 10:56

3 votes

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

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Tobias Fritzn

601

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

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Tobias Fritzn

601

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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 $\Pi_A$?

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Jonah

43

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4 votes

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Eigenvalues of a quantum state after partial tracing

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Heather

41

asked Sep 22, 2020 at 19:56

5 votes

2 answers

142 views

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

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Alice Munroe

53

asked Oct 20, 2020 at 0:21

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

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

How is quantum teleportation generalized to qudits?

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

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

How to take the limits of the sandwiched Renyi divergences?

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

How is a classical bipartite state written in quantum notation?

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

How to prove generalized Uhlmann's theorem?

Permutation invariant states have permutation invariant purifications - proof?

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

Positive semidefinite relationship after partial trace

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

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

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

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

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

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 $\Pi_A$?

Eigenvalues of a quantum state after partial tracing

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