Topic

Quantum relative entropy

10 records: 7 unsolved, 3 solved. Filter the catalog by this topic →

Additivity of the relative entropy of entanglement
Does the relative entropy of entanglement of every bipartite state equal its regularization, or is regularization genuinely necessary?
Solved
Bidirectional classical-communication cost of bipartite channel simulation
What is the asymptotic classical-communication cost of simulating a bipartite quantum channel with bidirectional classical communication and non-signalling assistance?
Unsolved
Amortization collapse for superchannel divergences
Does amortization collapse for the max-relative entropy and geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?
Unsolved
Ordinary-Petz fidelity remainder for relative-entropy data processing
Does the ordinary Petz recovery map give a universal fidelity remainder for monotonicity of quantum relative entropy?
Solved
Diamond-smoothed max-relative-entropy AEP for quantum channels
Does the max-relative entropy of finite-dimensional quantum channels satisfy an asymptotic equipartition property under uniform diamond-norm smoothing?
Unsolved
Umegaki relative entropy of local recovery
Does the conditional mutual information of every finite-dimensional tripartite state dominate its Umegaki relative entropy of local recovery?
Solved
Fixed-error parallel Stein lemma for quantum channels
Let \(\mathcal N,\mathcal M:\mathcal L(A)\to\mathcal L(B)\) be quantum channels on finite-dimensional systems.
Unsolved
Generalized Stein lemma for fully quantum channel resources
Let \(\mathcal N:\mathcal L(A)\to\mathcal L(B)\) be a finite-dimensional quantum channel.
Unsolved
Relative entropy of entanglement for two qubits
Find a closed formula for the relative entropy of entanglement of every two-qubit density operator \(\rho\), including an explicit closest separable state.
Unsolved
Square-root remainder in generalized quantum equipartition
Let \(H\) be a \(d\)-dimensional Hilbert space.
Unsolved