Multi-state imaginarity and coherence in qubit systems

• URL: http://arxiv.org/abs/2507.14878v1
• Date: Sun, 20 Jul 2025 09:34:57 GMT
• Title: Multi-state imaginarity and coherence in qubit systems
• Authors: Mao-Sheng Li, Rafael Wagner, Lin Zhang,
• Abstract summary: We provide a unitary-invariant framework to pinpoint imaginarity and coherence in sets of qubit states.<n>We also show that the set of imaginarity-free multi-states is not convex, and that third-order invariants completely characterize multi-state imaginarity of single-qubits but not of higher-dimensional systems.
• Score: 3.7112567233163003
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Traditionally, the characterization of quantum resources has focused on individual quantum states. Recent literature, however, has increasingly explored the characterization of resources in multi-states (ordered collections of states indexed by a varying parameter). In this work, we provide a unitary-invariant framework to pinpoint imaginarity and coherence in sets of qubit states: we prove that Bloch vectors must be coplanar to be imaginarity-free and colinear to be incoherent, yielding exact rank-based tests of coherence and imaginarity, and closed-form bounds for existing robustness quantifiers, all based on two-state overlaps only. We also show that the set of imaginarity-free multi-states is not convex, and that third-order invariants completely characterize multi-state imaginarity of single-qubits but not of higher-dimensional systems. As our main technical result, we show that every Bargmann invariant of single-qubit states is determined (up to conjugation) by two-state overlaps. Beyond qubits, we give purity and system-agnostic coherence witnesses from equality constraints on higher-order invariants and connect our results to practical protocols: characterization of partial distinguishability, spin-chirality detection, and subchannel discrimination.

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