Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).
Title resolution pending
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
citation-role summary
background 3
citation-polarity summary
fields
quant-ph 5years
2026 5verdicts
UNVERDICTED 5roles
background 3polarities
background 3representative citing papers
Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.
citing papers explorer
-
Quantum channel tomography: optimal bounds and a Heisenberg-to-classical phase transition
Quantum channel tomography query complexity transitions from Heisenberg scaling Θ(r d1 d2 / ε) at dilation rate τ=1 to classical scaling Θ(r d1 d2 / ε²) for τ ≥ 1+Ω(1).
-
Optimal Quantum State Testing Even with Limited Entanglement
Algorithms achieve near-optimal quantum state certification with limited entanglement (t=d^2 copies), plus similar results for mixedness testing and purity estimation, supported by lower bounds.
-
Probabilistic and approximate universal quantum purification machines
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
-
Quantum metrology of mixed states via purification
New purification-based reformulations of QCRB and HCRB connect mixed-state metrology bounds to those of purified states, enabling asymptotic attainment of HCRB or 2×QCRB via random channels and individual measurements.
-
Advances in quantum learning theory with bosonic systems
A concise review of sample complexities and methods for tomography and learning in continuous-variable quantum systems, with emphasis on Gaussian versus non-Gaussian states.