Field
Quantum Metrology
23 records: 21 unsolved, 2 solved. Filter the catalog by this field →
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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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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?
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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.
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Amortization collapse for superchannel divergences
Does amortization collapse for the geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?
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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?
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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?
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Gaussian-measurement equality with the Holevo bound
When does the optimal single-copy Gaussian-measurement cost equal the Holevo bound?
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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)?
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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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Parallel versus nested-adaptive superchannel discrimination
Can nested-adaptive strategies improve the Stein exponent for discriminating two finite-dimensional quantum superchannels?
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Weyl–Heisenberg-covariant SICs in every dimension
Does every finite dimension admit a symmetric informationally complete measurement that is a single Weyl–Heisenberg orbit?
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Statistical strength of CGLMP measurements
For every \(d\geq3\), do the standard CGLMP Fourier–phase measurements maximize the relative-entropy statistical strength against local realism among all projective \(d\)-outcome measurements on the fixed state \(\lvert\Phi_d\rangle=d^{-1/2}\sum_{j=0}^{d-1}\lvert j,j\rangle\), when the setting distribution is also optimized?
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Zauner-symmetric Weyl–Heisenberg SIC fiducials
Does every finite dimension admit a Weyl–Heisenberg SIC fiducial that is an eigenvector of a Zauner Clifford unitary?
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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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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?
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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.
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SIC-POVM existence in every dimension
Does a symmetric informationally complete positive-operator-valued measure exist in every finite dimension \(d\ge2\)?
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Maximum number of mutually unbiased bases
For each integer \(d\geq2\), determine the maximum number \(\mu(d)\) of pairwise mutually unbiased orthonormal bases of \(\mathbb C^d\).
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Optimal CGLMP measurements for a maximally entangled state
For every \(d\geq3\), do the standard Fourier–phase measurements optimize the CGLMP violation of the maximally entangled state among all projective \(d\)-outcome measurements?
Unsolved