Topic

Quantum estimation

Sparse Hamiltonian learning without short-time control
Can every polynomially sparse Hamiltonian be learned with Heisenberg-limited total evolution time when every oracle call has a fixed minimum duration?
Unsolved
Optimal dimension-free copy complexity of shadow tomography
Can list-dependent shadow tomography always achieve dimension-free copy complexity \(O(\log M/\varepsilon^2)\)?
Unsolved
Unknown-structure Hamiltonian learning from Gibbs states at all temperatures
Can every bounded-degree local Hamiltonian with unknown interaction support be learned efficiently from copies of its Gibbs state at any fixed inverse temperature?
Unsolved
Optimal single-copy tomography of fermionic Gaussian states
Can arbitrary mixed fermionic Gaussian states be learned to trace distance \(\varepsilon\) from \(\Theta(m^2/\varepsilon^2)\) copies without measurements across copies?
Unsolved
Optimal precision dependence of diamond-norm channel tomography
Does tomography of an arbitrary \(d\)-dimensional quantum channel in diamond norm require and suffice with \(\Theta(d^4/\varepsilon^2)\) channel uses?
Unsolved
Asymptotic metrology with quantum-controlled causal order
Does quantum control of causal order yield a persistent asymptotic metrological advantage over parallel access for some regular, finite-dimensional channel family?
Solved
Gaussian-measurement equality with the Holevo bound
When does the optimal single-copy Gaussian-measurement cost equal the Holevo bound?
Unsolved