Gaussian coherence-breaking channels and coherence measures
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Gaussian coherence-breaking channels and coherence measures Danxiang Wu1 · Kan He1 Received: 1 March 2020 / Accepted: 21 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We give a characterization of arbitrary n-mode Gaussian coherence-breaking channels (GCBCs) and construct a kind of Gaussian coherence measure based on the topic of GCBCs. We show the measure can be calculated conveniently. Keywords Quantum coherence · Gaussian coherence-breaking channels · Gaussian coherence measures
1 Introduction Quantum coherence is one of the fundamental topics of the quantum theory and has been developed as an important quantum resource in recent years (Ref. [1]). It had been linked to quantum entanglement in many quantum phenomena and plays an important role in the fields of quantum biology and quantum thermodynamics [2–8]. In finite-dimensional systems, the theory of quantum coherence has been undertaken extensively [9–19], for instance, quantifying coherence (see [1] and its relative references). As we know, continuous-variable (CV) quantum systems are fundamentally important from theoretical and experimental views, especially Gaussian systems. Recently, several researchers focused on the theory of quantifying quantum coherence of Gaussian states [15–28]. Xu [28] defined a Gaussian relative entropy of coherence for a Gaussian state. Buono et al. [15] studied geometric quantifiers of coherence for Gaussian states in terms of Bures and Hellinger distance from the set of incoherent Gaussian states. How can we find more coherence measures of Gaussian states? In the present paper, we will put up an interesting approach to quantify coherence of Gaussian states, which is calculated based on covariance matrices. Surprisingly, the
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Kan He [email protected] College of Mathematics, Institute of Applied Mathematics and Quantum Computing, Taiyuan University of Technology, Taiyuan 030024, People’s Republic of China 0123456789().: V,-vol
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definition of the measure arises from characterization of Gaussian coherence-breaking channels. The paper is organized as follows. In Sect. 2, we review the existing Gaussian measures introduced in [15–28]. In Sect. 3, we give a complete characterization of Gaussian coherence-breaking channels. In Sect. 4, we construct a new class of quantifiers of coherence of Gaussian states and discuss the properties of the quantifier. Furthermore, we show how to calculate the measure.
2 Review on quantifying quantum coherence In the section, let us recall some notations about the coherence theory. Definition 2.1 Let H be a d-dimensional Hilbert space, with the fixed specified basis d , a state ρ on H is incoherent if ρ = λ |ii|, otherwise, it is coherent. {|i}i=1 i i Denote by I the set of all incoherent states. The analogous definition can be extended to the infinite-dimensional space. Let T (H ) be the space of all trace-class operators on H , i.e., √ T (H ) = {T : T is a bounded linear operators on H with tr( T † T )
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