Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

Violations of Bell inequalities are better preserved by turbulent atmospheric channels than by comparable optical fibers in the scenario of copropagating entangled photons [A. A. Semenov and W. Vogel, Phys. Rev. A 81, 023835 (2010); arXiv:0909.2492]. Here we reexamine this result for the case of counterpropagation also considering the fact that each receiver registers so-called doubleclick events, which are caused by dark counts, stray light, and multi-photon entangled pairs. We show that advantages of the atmospheric links are feasible only for the copropagation scenario in the case of strong fluctuations of losses. For counterpropagation, the violations of Bell inequalities can be improved with an additional postselection procedure testing the channel transmittance.

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