Abstract
Coherence is associated with transient quantum states; in contrast, equilibrium thermal quantum systems have no coherence. We investigate the quantum control task of generating maximum coherence from an initial thermal state employing an external field. A completely controllable Hamiltonian is assumed allowing the generation of all possible unitary transformations. Optimizing the unitary control to achieve maximum coherence leads to a micro-canonical energy distribution on the diagonal energy representation. We demonstrate such a control scenario starting from a given Hamiltonian applying an external field, reaching the control target. Such an optimization task is found to be trap-less. By constraining the amount of energy invested by the control, maximum coherence leads to a canonical energy population distribution. When the optimization procedure constrains the final energy too tightly, local suboptimal traps are found. The global optimum is obtained when a small Lagrange multiplier is employed to constrain the final energy. Finally, we explore the task of generating coherences restricted to be close to the diagonal of the density matrix in the energy representation.
Highlights
The existence of coherence in a system is a signature of its quantum properties
Coherence underlies phenomena such as quantum interference and multipartite entanglement that play a central role in the applications of quantum thermodynamics and quantum information science [3,4]
The fulfilment of this task depends on the constraints imposed: Unconstrained optimization, (Section 3) maximum coherence with minimum energy invested (Section 4) or limiting the coherence to be close to the diagonal (Section 5)
Summary
The existence of coherence in a system is a signature of its quantum properties. Coherence is considered as a resource in many applications [1,2]. The issue addressed in this study is the optimal generation of coherence from an initial thermal state. Generating coherence from a passive state involves a cost in work. In this study we will use a distance metric D and C (see below) With these definitions we can first define a unitary control task to achieve maximum coherence. The present study incorporates the theory of quantum control to address a quantum task of optimizing coherence. The fulfilment of this task depends on the constraints imposed: Unconstrained optimization, (Section 3) maximum coherence with minimum energy invested (Section 4) or limiting the coherence to be close to the diagonal (Section 5)
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