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arXiv:2601.10979 · Physical Review A

Off-resonant preservation and generation of imaginarity in distributed scenarios

Si-Min Wang, Ming-Liang Hu, Heng Fan

quant-phSubmitted Jan 16, 2026• Announced Jan 19, 2026• 1 citation• Revised Jun 1, 2026 (v2)
v1 · Jan 16, 2026v2 · Jun 1, 2026
arXivHTMLPDF

Abstract

We study the nonlocal advantage of quantum imaginarity (NAQI) and distillable imaginarity of assistance (DIA), which treat imaginarity as a resource in distributed scenarios. For two qubits interacting with a lossy cavity, it is shown that both the NAQI and DIA can be well preserved for long times in the presence of large and symmetric detuning between the qubits and the cavity. Moreover, the off-resonant interaction generates a high degree of NAQI and DIA from the initial product states of two qubits having the same detunings and unequal couplings to the cavity. Based on the effective coupling of the qubits induced by the cavity mode, we explain the physical mechanism underlying the validity of this strategy. Our findings shed light on the role that off-resonant interactions have in the efficient control of imaginarity in distributed scenarios.

Journal reference
Phys. Rev. A 113, 052457 (2026)
DOI
10.1103/3jkw-tmbj
Comments
13 pages, 9 figures; Final version published in Phys. Rev. A

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Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity l1{l}_{1}l1​-norm and relative entropy, we derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not vice versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states.
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Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a fundamental advantage in state discrimination. We construct a set of five orthogonal three qubit pure states and show that the set is strongly nonlocal if and only if it includes imaginary components. Such a set becomes locally indistinguishable not only under local measurements but also against bipartite joint measurements. This enhanced robustness makes imaginarity a valuable resource for quantum cryptography since information encoded in these states remains secure against collaborative group attacks. Our results highlight a new operational role of complex numbers in quantum theory and establish imaginarity as a key enabler of cryptographic security. However, we reconstruct the set by replacing the only product state with a biseparable state whose shared entanglement between two parties nullifies the effect of imaginarity in exhibiting strong nonlocality. In fact, we show how entangling correlations between two distant parties can dilute the effect of imaginarity, and conversely, how imaginarity itself can mimic the role of entanglement. Nevertheless, the set spans a locally indistinguishable subspace, while its complement, in turn, produces distillable genuine entanglement. Notably, this is the smallest possible Unextendible Biseparable Basis (UBB) that resolves the open problem regarding the existence of a UBB of cardinality d2+d−1d^2+d-1d2+d−1 in d⊗3d^{\otimes 3}d⊗3. Our construction yields a highly powerful set, rich in resources from multiple perspectives of quantum information theory, including many-copy discrimination, unambiguous identification, entanglement creation from product state, and non-entangling perturbations.
Abstract The pivotal role of complex numbers in quantum mechanics underpins the resource theory of imaginarity. We investigate imaginarity dynamics in a single-qubit open system coupled to a non-Markovian environment. Crucially, cavity field detuning emerges as the dominant regulator, driving continuous conversion between the real and imaginary components of coherence. Nonzero detuning induces characteristic non-periodic oscillations of imaginarity between zero and maximal values, preventing complete decoherence at specific times. We establish that imaginarity resources stem from both intrinsic system evolution and environmental feedback. Significantly, detuning-driven imaginarity generation persists even in Markovian regimes, demonstrating its origin beyond environmental memory effects. These insights offer new perspectives for understanding and harnessing quantum coherence.