Spacetime Curvature and Quantum Information

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What is the relationship between space, time, and quantum information? This proposal is designed to answer this question, bringing together phenomena as varied and exotic as black holes, reference frames, thermodynamics, dark matter, polymers, holography, quantum information, cavity/circuit experiments in Quantum Electrodynamics, and quantum foundations. ***One side of the question concerns Black Holes, whose existence is all but guaranteed based on evidence from astronomy.  Black holes appear to be the ultimate repositories of information, fully absorbing it but radiating thermally in a manner that "erases" the information, violating basic principles of quantum physics. To resolve this contradiction and understand how quantum effects influence spacetime, we must understand how black holes behave thermodynamically. I will pioneer a new approach to this problem I call "Black Hole Chemistry", based on my recent work showing that vacuum energy can cause black holes to behave like chemical systems, with liquid/gas-type phase transitions, triple points, and more. "Black hole chemistry" will likely overturn our standard notions of gravitational thermodynamics, particularly with regards to the ideas about holography that emerge from string theory. I will forge ahead to examine the implications of black hole chemistry for early-universe cosmology, the proposed dual relationship between gravity and condensed-matter systems, and the appearance of possible new phenomena such as transitions into a new glass phase and the merging of 4 distinct black hole phases into a "quadruple critical point".***The other side of the question is how relativistic effects influence quantum information tasks. Known as Relativistic Quantum Information (RQI) this new field has in the past 10 years developed from a study of foundational questions to a point where actual experiments can be contemplated. I propose to advance RQI to the next level of genuine confrontation with experiment, using methods my group has developed in the past 5 years. Various classes of experiments will be proposed, constructed, and refined. One class will probe how accelerating detectors actually get hot (a long-standing prediction called the Unruh effect), using cavities and circuits as simulation tools. Another class will exploit the new technique of Quantum Control to study a quantum version of the gravitational slowdown of light, the first confrontation of RQI with experiment in a gravitational setting. A third class of experiments will consider applications of RQI, such as non-demolition photon measurements, a quantum seismograph, harvesting entanglement using cavities, and various aspects of metrology.****The scope of this research ranges from the largest physical scales to the smallest, and from abstract mathematical questions to applied research in the lab.  Its results will provide us with a new understanding of gravity and the quantum.********