Coherent Dynamics

Shaoying Yin, Shutian Liu, Jie Song +1 more

The Markovian and non-Markovian dynamics of quantum coherence, including single-spin coherence, two-spin coherence, and its distribution (collective and localized coherence), are investigated in the $XX$ spin chain with three-spin interaction. We find that the single-spin and localized coherence do not decrease but increase with time, which makes the dynamic evolution of the two-spin coherence more robust than entanglement and quantum discord. The three-spin interaction can lower the values of quantum coherence in Markovian evolution and heighten the oscillation frequency of quantum coherence in non-Markovian evolution because it can speed up the flow of coherence information. Finally, the trade-off relation between the collective and the localized coherence is clearly shown in their dynamic evolution. Thanks to the coherence trade-off, we find the substitution of localized coherence for collective coherence in dominating the dynamics of the two-spin coherence.

Robert B. Griffiths

Sunho Kim, Chunhe Xiong, Asutosh Kumar +2 more

Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate definition of incoherent operations induced via coherence measures and quantify dynamical coherence based on this definition. Finally, we apply our proposed definition to quantify POVM-based dynamical coherence.

V. M. Akulin, N. V. Karlov

Zi-yi Mai, Chang‐shui Yu

Coherence is the most fundamental quantum resource in quantum information processing. How fast a physical system gets coherence or decoherence is a critical ingredient. We present an attainable quantum speed limit based on the variation of quantum coherence subject to a dynamical process. It indicates that for a two-dimensional quantum state, one can always find corresponding dynamics driving it to evolve along the geodesic to another state with certain coherence variation. As applications, we study the coherence quantum speed limits of the dephasing and dissipative dynamics. It is shown that the dephasing dynamics can saturate our coherence quantum speed limit, and the decoherence of the state with identical populations will be faster than others. However, the dissipative dynamics have the opposite behavior. In addition, we illustrate a stronger tightness of our bound for the mentioned dynamics by comparison.

Kun Zhang, Hai-Long Shi, Xiao-Hui Wang +1 more

Quantum coherence is a central resource in quantum information science, yet general frameworks and constraints governing its dynamics remain limited. Although quantum coherence lacks a general monotonicity law, we establish an exact integral fluctuation theorem (FT) for coherence dynamics, formulated in terms of Kirkwood-Dirac (KD) quasiprobability trajectories and valid for arbitrary initial states and dynamics. This integral FT deviates from the standard unit-valued form, and the complex deviation, termed the anomaly, quantifies a weighted overlap between the residual final-state coherence and the coherence generated from the dephased input. The real part of the anomaly yields bounds on coherence change, while its imaginary part constrains the second-order moment of the stochastic coherence change weighted by the imaginary parts of the KD quasiprobabilities. Our results establish general statistical constraints on coherence dynamics, demonstrating the utility and broad applicability of FTs for studying quantum-resource dynamics.