Generally quantum processes tend to mix the pure input states and degrade the original coherence. Such processes display exactly the trade-offs between the coherence and the mixedness. In this paper, we present trade-offs between the coherence measures (l2 norm of coherence, coherence via skew information, geometric measure of coherence) and the mixedness (normalized linear entropy mixedness, geometric measure of mixedness, mixedness via skew information). The evolution of these trade-offs are also investigated under four quantum noise channels: the bit flip, phase flip, depolarizing and amplitude damping channels.
Generally quantum processes tend to mix the pure input states and degrade the original coherence. Such processes display exactly the trade-offs between the coherence and the mixedness. In this paper, we present trade-offs between the coherence measures (l2 norm of coherence, coherence via skew information, geometric measure of coherence) and the mixedness (normalized linear entropy mixedness, geometric measure of mixedness, mixedness via skew information). The evolution of these trade-offs are also investigated under four quantum noise channels: the bit flip, phase flip, depolarizing and amplitude damping channels.
Abstract Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the l 2 norm coherence, conditional von Neumann entropy and Wigner–Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise.
We investigate the relationships among the wave property, particle property and mixedness of quantum states based on the lp-norm coherence. By conforming that the lp-norm coherence is an appropriate measure of wave property and introducing a measure of particle property based on the differences between the maximal l2-norm coherence and the general l2-norm coherence, we present tradeoff relationships among the wave, particle and mixedness of quantum states. For 1<= p <2, we establish two kinds of tradeoffs of the wave, particle and mixedness with respect to the upper and lower bounds of the lp-norm coherence given by the l2-norm coherence. These trade relations give rise to compressive understanding of the intrinsic connections among the wave, particle and mixedness of quantum states, and cover some existing results as particular ones.
Abstract As an important resource, quantum coherence is one of the fundamental features of the quantum world. It is essential to understand the relationship between the resource and the mixedness of an open quantum system. We present complementary relations between the l p ( 1 ⩽ p < 2 ) norm of coherence and the normalized linear entropy mixedness. We then study the geometry of the complementary relations for Bell-diagonal states, as well as the evolutions of Werner and isotropic states under bit flip, phase flip, bit-phase flip, depolarizing, generalized amplitude damping and amplitude damping channels. Our results include some existing conclusions as special cases.
We investigate the trade-off relations between imaginarity and mixedness in arbitrary d-dimensional quantum systems. For given mixedness, a quantum state with maximum imaginarity is defined to be a "maximally imaginary mixed state" (MIMS). By using the l1 norm of imaginarity and the normalized linear entropy, we conclusively identify the MIMSs for both qubit and qutrit systems. For high-dimensional quantum systems, we present a comprehensive class of MIMSs, which also gives rise to complementarity relations between the 1-norm of imaginarity and the 1-norm of mixedness, as well as between the relative entropy of imaginarity and the von Neumann entropy. Furthermore, we examine the evolution of the trade-off relation for single-qubit states under four specific Markovian channels: bit flip channel, phase damping channel, depolarizing channel and amplitude damping channel.
Abstract Quantum coherence is a relevant resource for various quantum information processing tasks, but it is fragile since it is generally affected by environmental noise. This is reflected in the loss of purity of the system, which in turn limits the amount of quantum coherence of it. As a consequence, a complementarity relation between coherence and mixedness arises. Previous works characterize this complementarity through inequalities between the ℓ 1-norm of coherence and linear entropy, and between the relative entropy of coherence and von Neumann entropy. However, coherence–mixedness complementarity is expected to be a general feature of quantum systems, regardless of the measures used. Here, an alternative approach to coherence–mixedness complementarity, based on majorization theory, is proposed. Vectorial quantifiers of coherence and mixedness, namely the coherence vector and the spectrum, respectively, are used, instead of scalar measures. A majorization relation for the tensor product of both vectorial quantifiers is obtained, capturing general aspects of the trade-off between coherence and mixedness. The optimal bound for qubit systems and numerical bounds for qutrit systems are analyzed. Finally, coherence–mixedness complementarity relations are derived for a family of symmetric, concave and additive functions. These results provide a deeper insight into the relation between quantum coherence and mixedness.
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l 1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α -entropies, while the bit flit channel does change for some special cases.