Entangled measurements are necessary for optimal tomography of mixed fermionic Gaussian states and of bosonic Gaussian states near the vacuum

arXiv:2609.23189 · quant-ph, math-ph, math.MP · Submitted 2026-09-19 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-19

Updated: 2026-09-19

Terminology

• Trace — 77× in this paper · explained in 2 episodes
• Trace Distance — 22× in this paper · explained in 3 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Fisher Information — 8× in this paper · explained in 3 episodes
• Adaptivity — 6× in this paper · explained in 1 episode
• Calibration — 6× in this paper · explained in 7 episodes
• Entanglement — 4× in this paper · explained in 3 episodes
• Gibbs State — 4× in this paper · explained in 2 episodes
• Non-Gaussianity — 4× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• Shadow Tomography — 2× in this paper · explained in 4 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Heisenberg Scaling — 1× in this paper · explained in 4 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes
• Process tomography — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Self-consistency — 1× in this paper · explained in 2 episodes
• Wigner function — 1× in this paper · explained in 2 episodes

Sources

• Optimal tomography of bosonic and fermionic Gaussian states
• Triply efficient shadow tomography
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Learning quantum states and unitaries of bounded gate complexity
• The log log jam in Gaussian state tomography
• What resources are needed for optimal learning of bosonic Gaussian states?
• Fermionic partial tomography via classical shadows
• Energy-independent tomography of Gaussian states
• Exponential separations between learning with and without quantum memory
• When Does Adaptivity Help for Quantum State Learning?
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Universally Fisher-Symmetric Informationally Complete Measurements
• Classical simulation of noninteracting-fermion quantum circuits
• Lagrangian representation for fermionic linear optics
• Fermionic Gaussian states: an introduction to numerical approaches
• A random purification channel for arbitrary symmetries with applications to fermions and bosons
• Tight Lower Bounds for State Tomography with Limited Entanglement
• Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
• State estimation for large ensembles
• $L$-systems and the Lov'asz number

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