Topic

Quantum relative entropy

12 records: 9 unsolved, 3 solved. Filter the catalog by this topic →

Uniform modified log-Sobolev constant for one-dimensional Gibbs samplers
Do normalized one-dimensional Chen–Kastoryano–Gilyén Gibbs samplers have a positive modified log-Sobolev constant uniformly in system size at every fixed finite temperature?
Unsolved
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
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
Amortization collapse for superchannel divergences
Does amortization collapse for the geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?
Unsolved
Exact privacy-amplification exponent under relative-entropy security
What is the optimal exponential rate of decay of relative-entropy insecurity achievable by two-universal hashing against quantum side information at every positive extraction rate below the conditional entropy?
Unsolved
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
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
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
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
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