In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state
ρs′ as the input to a quantum channel
Λ, instead of the original state
ρs, can yield an output state
Λ(ρs′) whose coherence fraction exceeds that of
Λ(ρs). We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map
E to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.
We analyze quantum coherence generated by non-interacting magnons in a ferromagnetic spin chain described by the isotropic Heisenberg model. The exact expression derived for the reduced density operator of an arbitrary subsystem reveals that single-site coherence vanishes, while maximal coherence arises in a pure single-mode magnon state. Remarkably, this maximum depends solely on the number of coherently superposed microstates. Based on this property, we introduce coherence-based definitions of entropy, temperature, and heat capacity, establishing a formal analogy with standard thermodynamic quantities.
Considering the quantum memory channels, we study the dynamical evolutions of quantum coherence and quantum mutual information as measures of quantum correlations under the actions of different decoherence channels on some bipartite initial states. Under any quantum operation or process occurring in a noisy environment, quantum correlations exhibit behavior that does not increase due to the system interacting with its environment. We state that for such a case the decrement of quantum correlations can be improved by the suitable choice of the initial states and by adjusting the parameters. Thus quantum correlations can be partially preserved against the action of the environment. It can be shown that optimal conditions to prohibit the partial loss in quantum coherence and quantum mutual information for performing any quantum information task may be generated by the memory.
We investigate the behavior of thermal quantum coherence in the Heisenberg XXX model for a two-qubit system placed in independently controllable Inhomogeneous magnetic fields applied to two qubits respectively. We discuss the behavior of quantum coherence by systematically varying the coupling parameter, magnetic field, and temperature for both ferromagnetic and antiferromagnetic cases. The results show the interesting behavior of quantum coherence in a certain range of parameters. Generally, it is observed that quantum correlations decay with temperature, but in the ferromagnetic case with uniform magnetic interaction, it rises with temperature up to a certain threshold value and ultimately it decreases its value to zero. Moreover, it is observed that preserving the quantum coherence for small temperatures is very hard with the increasing magnetic field because, at small temperatures, quantum coherence decays sharply with the increase in magnetic field whereas at larger temperatures it decays completely at fairly large values of the magnetic field. The variation of quantum coherence with uniform magnetic field in the antiferromagnetic case is observed to be Gaussian for larger temperature but at zero or nearly zero temperature, it behaves as a constant function for uniform magnetic field up to a threshold value and then decays to zero with an infinite slope. This shows the signature of quantum phase transition from quantum nature to classicality.
Abstract Average steered coherence (ASC) reflects the nonlocal property of a state from a fundamental aspect and the steerable states achieve a nonlocal advantage of quantum coherence (NAQC) when the ASC exceeds a threshold. We explore the ASC in both the spin-1 XXZ model with Dzyaloshinskii–Moriya (DM) and Kaplan–Shekhtman-Entin–Wohlman–Aharony (KSEA) interactions and the dimerized XXZ model. For the first model, it is found that the ASC in the thermal state can be enhanced by tuning the anisotropic parameter and the DM and KSEA interactions; while for the second model, the ASC can be enhanced by tuning the J 2 interaction and there exists a temperature plateau at which it remains almost the constant. Besides, for both the spin-1 models, a NAQC can always be achieved by optimizing the involved controlling parameters.
The coherence power of a quantum channel, that is, its maximum ability to increase the coherence of input states, is a fundamental concept within the framework of the resource theory of coherence. In this note we discuss various possible definitions of coherence power and coherence rate and their basic properties. Then we prove that the coherence power of a unitary operator acting on a qubit, computed with respect to the l1-coherence measure, can be calculated by maximizing its coherence gain over pure incoherent states. We proceed to show that this result fails in the general case, that is, the maximal coherence gain is found when acting on a state with non-vanishing coherence in the case of the l1-coherence and dimension N > 2, the relative entropy of coherence and the geometric measure of coherence.