Coherence arises from the superposition principle and plays a key role in quantum mechanics. Recently, Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] established a rigorous framework for quantifying the coherence of finite-dimensional quantum states. In this work we provide a framework for quantifying the coherence of Gaussian states and explicitly give a coherence measure for Gaussian states based on the relative entropy.
Coherence arises from the superposition principle and plays a key role in quantum mechanics. Recently, Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] established a rigorous framework for quantifying the coherence of finite-dimensional quantum states. In this work we provide a framework for quantifying the coherence of Gaussian states and explicitly give a coherence measure for Gaussian states based on the relative entropy.
Quantum Physics
The notion that particles have properties of waves lies at the heart of quantum mechanics. When quantum systems interact, their interaction can be described in terms of interfering waves, whose coherence is of utmost importance in working out how these waves ultimately interfere. Determining how much coherence there is in a system or how much is required for a particular process is difficult to quantify, though. Baumgratz et al. present a rigorous mathematical framework for the quantification of coherence and identify intuitive and easily computable measures that can be used to compute it. They argue that having such a quantifiable metric will have important implications for describing energy transfer processes or transferring quantum information between quantum elements.
Phys. Rev. Lett. 10.1103/PhysRevLett.113.140401 (2014).
The notion of measurement is of both foundational and instrumental significance in quantum mechanics, and coherence destroyed by measurements (decoherence) lies at the very heart of quantum to classical transition. Qualitative aspects of this spirit have been widely recognized and analyzed ever since the inception of quantum theory. However, axiomatic and quantitative investigations of coherence are attracting great interest only recently with several figures of merit for coherence introduced [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. While these resource theoretic approaches have many appealing and intuitive features, they rely crucially on various notions of incoherent operations which are sophisticated, subtle, and not uniquely defined, as have been critically assessed [Chitambar and Gour, Phys. Rev. Lett. 117, 030401 (2016)]. In this paper, we elaborate on the idea that coherence and quantum uncertainty are dual viewpoints of the same quantum substrate, and address coherence quantification by identifying coherence of a state (with respect to a measurement) with quantum uncertainty of a measurement (with respect to a state). Consequently, coherence measures may be set into correspondence with measures of quantum uncertainty. In particular, we take average quantum Fisher information as a measure of quantum uncertainty, and introduce the corresponding measure of coherence, which is demonstrated to exhibit desirable properties. Implications for interpreting quantum purity as maximal coherence, and quantum discord as minimal coherence, are illustrated.
We investigate the coherence measures induced by fidelity and trace norm, based on the coherence quantification recently proposed by Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of the measurement condition. We find that the trace norm of coherence can act as a measure of coherence for qubits and some special class of qutrits with some restrictions on the incoherent operators, while the general case needs to be explored further.
Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory. Baumgratz, Cramer and Plenio established a rigorous framework (BCP framework) for quantifying coherence [Baumgratz T, Cramer M and Plenio M B Phys. Rev. Lett. 113 140401 (2014)]. In the present paper, under the BCP framework we provide two classes of coherence measures based on the sandwiched Rényi relative entropy. We also prove that we cannot get a new coherence measure f ( C (·)) by a function f acting on a given coherence measure C .
Abstract Baumgratz, Cramer and Plenio established a rigorous framework (BCP framework) for quantifying the coherence of quantum states (2014, Phys. Rev. Lett. 113 , 140401). In BCP framework, a quantum state is called incoherent if it is diagonal in the fixed orthonormal basis, and a coherence measure should satisfy some conditions. For a fixed orthonormal basis, if a quantum state ρ has nonzero imaginary part, then ρ must be coherent. How to quantitatively characterize this fact? In this work, we show that any coherence measure C in BCP framework has the property C ( ρ ) − C (Re ρ )≥0 if C is invariant under state complex conjugation, i.e. C ( ρ ) = C ( ρ *), here ρ *is the conjugate of ρ , Re ρ is the real part of ρ . If C does not satisfy C ( ρ ) = C ( ρ *), we can define a new coherence measure C ′ ( ρ ) = 1 2 [ C ( ρ ) + C ( ρ * ) ] such that C ′ ( ρ ) = C ′ ( ρ * ) . We also establish some similar results for bosonic Gaussian states.
Abstract The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality.