Permutationally Invariant Quantum State Tomography for Fermions

• URL: http://arxiv.org/abs/2607.23579v1
• Date: Sun, 26 Jul 2026 10:04:25 GMT
• Title: Permutationally Invariant Quantum State Tomography for Fermions
• Abstract summary: We develop a tomography protocol for permutation-invariant fermionic many-body states with U(1) particle-number symmetry.<n>We show that any such state is completely determined by the distribution of the total particle number.<n>More generally, the protocol reconstructs the permutation-symmetrized component of arbitrary U(1)-symmetric fermionic states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum state tomography provides complete information about a quantum state, but its measurement cost generally grows exponentially with system size. In many-particle quantum simulators, this challenge is further compounded by the limited accessibility of local measurements and controls. Here we develop a tomography protocol for permutation-invariant fermionic many-body states with U(1) particle-number symmetry. We show that any such state is completely determined by the distribution of the total particle number and the occupation of a single collective mode within each particle-number sector, both of which are accessible in current ultracold-atom experiments. The number of required observables scales only linearly with the system size. More generally, the protocol reconstructs the permutation-symmetrized component of arbitrary U(1)-symmetric fermionic states, which can still encode nontrivial many-body and state-level structure beyond conventional few-body observables. We demonstrate this protocol in interacting non-Gaussian states of the complex Sachdev-Ye-Kitaev model and in free-fermion chains across a Lifshitz transition. This framework opens a route toward information-theoretic characterization of strongly correlated itinerant quantum matter in experimentally realistic fermionic quantum simulators.

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