Field
Quantum Metrology
18 records: 16 unsolved, 2 solved. Filter the catalog by this field →
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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 -
Amortization collapse for superchannel divergences
Does amortization collapse for the geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?
Unsolved -
Parallel versus nested-adaptive superchannel discrimination
Can nested-adaptive strategies improve the Stein exponent for discriminating two finite-dimensional quantum superchannels?
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 -
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 -
Gaussian-measurement equality with the Holevo bound
When does the optimal single-copy Gaussian-measurement cost equal the Holevo bound?
Unsolved -
Convergence of the JRF iteration for mixed-state discrimination
Does the Ježek–Řeháček–Fiurášek (JRF) iteration, initialized by the uniform POVM, converge to a globally optimal minimum-error measurement for every finite ensemble containing mixed quantum states?
Unsolved -
Sample complexity of low-rank tomography with Pauli measurements
How many copies of an unknown low-rank \(N\)-qubit state does tomography with Pauli measurements need?
Unsolved -
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?
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Optimal dimension-free copy complexity of shadow tomography
Can list-dependent shadow tomography always achieve dimension-free copy complexity \(O(\log M/\varepsilon^2)\)?
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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?
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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?
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Single-copy identity testing of local Gibbs states
What is the minimax copy complexity of identity testing two unknown \(k\)-local Gibbs states using only measurements on individual copies?
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Single-seed post-processing of Gaussian POVM densities
Is every POVM with Gaussian density a classical post-processing of one displaced Gaussian seed?
Solved -
LOCC discrimination of three maximally entangled states
Can every set of three orthogonal maximally entangled pure states on \(\mathbb C^d\otimes\mathbb C^d\), for every integer \(d\geq4\), be distinguished exactly from one copy using unrestricted two-way local operations and classical communication (LOCC)?
Unsolved -
Chernoff exponents under separable and LOCC tests across copies
Determine the optimal symmetric discrimination exponents for two faithful noncommuting states when measurements must be separable across copies or implemented by local operations and classical communication (LOCC) among the copies.
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Advantage of fully general superchannel-discrimination strategies
Can a fully general adaptive strategy attain a larger Stein exponent than every nested-adaptive strategy for discriminating two quantum superchannels?
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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