Hybrid quantum dot-oscillator systems have become attractive platforms to inspect quantum coherence effects at the nanoscale. Here, we investigate a Cooper-pair splitter setup consisting of two quantum dots, each linearly coupled to a local resonator. The latter can be realized either by a microwave cavity or a nanomechanical resonator. Focusing on the subgap regime, we demonstrate that cross-Andreev reflection, through which Cooper pairs are split into both dots, can efficiently cool down simultaneously both resonators into their ground state. Moreover, we show that a nonlocal heat transfer between the two resonators is activated when opportune resonance conditions are matched. The proposed scheme can act as a heat-pump device with potential applications in heat control and cooling of mesoscopic quantum resonators. Nonlocality [1, 2] and quantum correlations [3] are at the heart of many quantum technologies [4][5][6]. In hybrid quantum dot devices, Cooper pairs are a source of correlated electrons and their nonlocal splitting has experimentally [7][8][9][10][11][12][13][14][15][16][17] and theoretically [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] drawn much attention over the last few years. In particular, the nonlocal breaking of the particlehole symmetry in such Cooper-pair splitters (CPSs) gives rise to peculiar thermoelectric effects [33][34][35][36]. On the other hand, hybrid cavity quantum electrodynamics (cQED) devices are suited for correlating few-level systems over a distance [37][38][39][40][41][42]. Such cQED devices have applications in the readout of charge [43][44][45][46][47][48][49], spin [50][51][52][53][54], and valley-orbit states [55,56]. Ground-state cooling of mechanical resonators in hybrid [57] and optomechanical [58,59] systems has been demonstrated, and a cooling scheme based on local Andreev reflection has been recently proposed [60,61]. The cooling of vibrational degrees of freedom due to quantum coherences has been also investigated in nanoelectromechanical systems [62]. Combining CPSs with microwave cavities or mechanical resonators opens up new avenues to tailor energy and heat flows in nanodevices [63-65] by exploiting quantum coherence.In this Letter, we consider a CPS in a double-quantum-dot setup with each dot linearly coupled to a local resonator, constituted by either a microwave cavity [46,48,51,[66][67][68][69] or a mechanical oscillator [70-73], see Fig. 1(a). We demonstrate that this system can cool efficiently and simultaneously the oscillators down to their ground state, and in addition generate a coherent transfer of photons, and hence heat, between the two originally uncoupled cavities. This interaction arises from a strong coupling between the dots and the superconducting lead, and has a purely nonlocal origin due to cross-Andreev reflection. Subsequent, we discuss the underlying physical mechanism following the lines of Ref. 74, where a single quantum dot system in the single-atom lasing regime has been investigated.For large intradot Coulomb inter...