Fundamental limitations in the purifications of tensor networks

We show a fundamental limitation in the description of quantum many-body mixed states with tensor networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.

Reconstructing the last interglacial at Summit, Greenland: Insights from GISP2

The Eemian (last interglacial, 130-115 ka) was likely the warmest of all interglacials of the last 800 ka, with summer Arctic temperatures 3-5 degrees C above present. Here, we present improved Eemian climate records from central Greenland, reconstructed from the base of the Greenland Ice Sheet Project 2 (GISP2) ice core. Our record comes from clean, stratigraphically disturbed, and isotopically warm ice from 2,750 to 3,040 m depth. The age of this ice is constrained by measuring CH_4 and delta O^18 of O_2, and comparing with the historical record of these properties from the North Greenland Ice Core Project (NGRIP) and North Greenland Eemian Ice Drilling (NEEM) ice cores. The d^18 O_ice, d^15N of N_2, and total air content for samples dating discontinuously from 128 to 115 ka indicate a warming of similar to 6 degrees C between 127-121 ka, and a similar elevation history between GISP2 and NEEM. The reconstructed climate and elevation histories are compared with an ensemble of coupled climate-ice-sheet model simulations of the Greenland ice sheet. Those most consistent with the reconstructed temperatures indicate that the Greenland ice sheet contributed 5.1 m (4.1-6.2 m, 95% credible interval) to global eustatic sea level toward the end of the Eemian. Greenland likely did not contribute to anomalously high sea levels at ~127 ka, or to a rapid jump in sea level at ~120 ka. However, several unexplained discrepancies remain between the inferred and simulated histories of temperature and accumulation rate at GISP2 and NEEM, as well as between the climatic reconstructions themselves.