Abstract The resource‐theoretic frameworks for quantum imaginarity have been developed in recent years. Within these frameworks, many imaginarity measures for finite‐dimensional systems have been proposed. However, for imaginarity of Gaussian states in continuous‐variable (CV) systems, there are only two known Gaussian imaginarity measures, which exhibit prohibitive computational complexity when applied to multi‐mode Gaussian states. In this paper, a computable Gaussian imaginarity measure is proposed for ‐mode Gaussian systems. The value of is simply formulated by the displacement vectors and covariance matrices of Gaussian states. A comparative analysis of with existing two Gaussian imaginarity measures indicates that can be used to detect imaginarity in any ‐mode Gaussian states more efficiently. As an application, the dynamics behavior of ‐mode Gaussian states is studied in Gaussian Markovian noise environments for two‐mode CV system by utilizing . Moreover, it is proved that, can induce a quantification of any ‐multipartite multi‐mode CV systems which satisfies all requirements for measures of multipartite multi‐mode Gaussian correlations, which unveils that, ‐mode Gaussian imaginarity can also be regarded as a kind of multipatite multi‐mode Gaussian correlation and is a multipartite Gaussian quantum resource.
Abstract The resource‐theoretic frameworks for quantum imaginarity have been developed in recent years. Within these frameworks, many imaginarity measures for finite‐dimensional systems have been proposed. However, for imaginarity of Gaussian states in continuous‐variable (CV) systems, there are only two known Gaussian imaginarity measures, which exhibit prohibitive computational complexity when applied to multi‐mode Gaussian states. In this paper, a computable Gaussian imaginarity measure is proposed for ‐mode Gaussian systems. The value of is simply formulated by the displacement vectors and covariance matrices of Gaussian states. A comparative analysis of with existing two Gaussian imaginarity measures indicates that can be used to detect imaginarity in any ‐mode Gaussian states more efficiently. As an application, the dynamics behavior of ‐mode Gaussian states is studied in Gaussian Markovian noise environments for two‐mode CV system by utilizing . Moreover, it is proved that, can induce a quantification of any ‐multipartite multi‐mode CV systems which satisfies all requirements for measures of multipartite multi‐mode Gaussian correlations, which unveils that, ‐mode Gaussian imaginarity can also be regarded as a kind of multipatite multi‐mode Gaussian correlation and is a multipartite Gaussian quantum resource.
We propose a quantification CνGn of n-mode Gaussian coherence. The value of CνGn only depends on the covariance matrices and displacement vectors of continuous-variable states without any optimization procedures, and thus is easily calculated. For n=1, CνG1 is a proper Gaussian coherence measure of single-mode CV system. For n≥2, CνGn is invariant under any permutation of submodes, nonincreasing under any n-mode local incoherent Gaussian channels, vanishes at incoherent Gaussian states, and, satisfies the unification condition and the hierarchy condition that a multi-partite quantum correlation measure should obey. Thus CνGn is a multi-partite Gaussian correlation measure, which reveals, though the quantum coherence lives in single-partite systems, that the multi-mode coherence for continuous-variable systems can be regarded as a multipartite Gaussian correlation between modes, and such multi-partite Gaussian correlation is also a quantum resource. Moreover, we show that CνGn is completely monogamous as a multipartite Gaussian correlation measure. This means that the n-mode Gaussian coherence subjects to the principles of resource allocation. In addition, CνGn is an upper bound of the geometric-based single-mode Gaussian coherence measure CBu by the Bures distance at pure Gaussian states of mode ≤2 and can be used to detect coherence in any n-mode Gaussian states more efficiently.
It is a long-standing debate that why quantum mechanics uses complex numbers but not real numbers only. To address this topic, in recent years, the imaginarity theory has been developed in the way of quantum resource theory. However, the existing imaginarity theory mainly focuses on the quantum systems with finite dimensions. Gaussian states are widely used in many fields of quantum physics, but they are in the quantum systems with infinite dimensions. In this paper we establish a resource theory of imaginarity for bosonic Gaussian states. To do so, under the Fock basis, we determine the real Gaussian states and real Gaussian channels in terms of the means and covariance matrices of Gaussian states. Also, we provide two imaginary measures for Gaussian states based on the fidelity.
Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.
ABSTRACT In this work, we develop an experimentally accessible framework for quantifying imaginarity resources in composite quantum systems. We first formulate an observable‐based imaginarity measure using expectation values of antisymmetric Hermitian observables, thereby identifies the minimal observable sector required for evaluating imaginarity. By extending the trace‐norm imaginarity measure to multipartite systems, we introduce local imaginarity and imaginarity correlation to distinguish local and correlation contributions of imaginarity resources. We further establish observable representations for these quantities and investigate their evaluation using incomplete measurements through truncated measures based on the accessible antisymmetric sector. The performance of the truncated scheme is quantified by analyzing the retained observable ratio, lower‐bound recovery, and finite‐shot statistical convergence. Numerical investigations on qubit and qutrit systems demonstrate the behavior of local and correlation imaginarity in nonextremal states, higher‐dimensional systems, and under phase‐damping noise. Finally, we reveal a quantitative connection between imaginarity correlation and entanglement, derive an upper bound, and show that imaginarity correlation can serve as an experimentally accessible witness of entanglement. Our results provide an operational framework for characterizing and measuring imaginarity resources in realistic quantum systems.
In this paper, a computable multipartite multimode Gaussian quantum correlation measure M(k) is proposed for any k-partite continuous-variable (CV) systems with k≥2. M(k) depends only on the covariance matrix of CV states, is invariant under any permutation of subsystems, is a quantification without ancilla problem, nonincreasing under k-partite local Gaussian channels (particularly, invariant under k-partite local Gaussian unitary operations), vanishes on k-partite product states. For a k-partite Gaussian state ρ, M(k)(ρ)=0 if and only if ρ is a k-partite product state. Thus, for the bipartite case, M=M(2) is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover, M(k) satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. M(k) is not bipartite like monogamous, but, M(k) is complete monogamous and tight complete monogamous.
In this paper, definitions of the unification condition, the hierarchy condition, and three kinds of monogamy relations for multipartite quantum correlation measures are given and discussed. A computable multipartite multimode Gaussian quantum correlation measure M(k) is proposed for any k-partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of M(k) only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under k-partite local Gaussian channels (particularly, invariant under k-partite locally Gaussian unitary operations), and vanishes on k-partite product states. For a k-partite Gaussian state $\ensuremath{\rho}, {\mathcal{M}}^{(k)}(\ensuremath{\rho})=0$ if and only if $\ensuremath{\rho}$ is a k-partite product state. Moreover, M(k) satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that M(k) is not strongly monogamous but completely monogamous and tightly monogamous.