Talks

It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here we show that this belief may or may not be true depending on a particular code. To this end, we characterize a tradeoff between the code distance d quantifying the number of correctable errors, and geometric entanglement of logical states quantifying their maximal overlap with product states or more general "topologically trivial" states. The maximum overlap is shown to be exponentially small in d for three families of codes: (1) low-density parity check (LDPC) codes with commuting check operators, (2) stabilizer codes, and (3) codes with a constant encoding rate. Equivalently, the geometric entanglement of any logical state of these codes grows at least linearly with d. On the opposite side, we also show that this distance-entanglement tradeoff does not hold in general. For any constant d and k (number of logical qubits), we show there exists a family of codes such that the geometric entanglement of some logical states approaches zero in the limit of large code length. This work was done by the collaboration with Sergey Bravyi, Zhi Li, and Beni Yoshida. (https://arxiv.org/abs/2405.01332)

Static patch holography is a conjectured duality between the static patch of an observer in de Sitter spacetime and a quantum theory defined on its (stretched) cosmological horizon. We illustrate from entanglement wedge reconstruction how a closed and connected de Sitter spacetime can emerge in this framework from the entanglement between the two holographic screens of two antipodal observers. In holographic spacetimes, a direct scattering in the bulk may not have a local boundary analog, imposing the existence of O(1/G) mutual information on the boundary. This statement is formalized by the connected wedge theorem, which is expected to hold beyond the AdS/CFT correspondence from which it originates. We consider scatterings in the static patch of an observer. We argue that for static patch holography to be consistent with the connected wedge theorem, causality on the stretched horizon should be induced from null infinity. In particular, signals propagating in the static patch are associated with fictitious local operators at null infinity. We present a sketch of proof of the connected wedge theorem in asymptotically de Sitter spacetime using induced causality.