Holographic measurement and bulk teleportation

Abstract

Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion A of the boundary theory modify the bulk dual spacetime. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region Ac that are cut off by end-of-the-world branes. Using a bulk calculation in AdS3 and tensor network models of holography (in particular, the HaPPY code and random tensor networks), we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of A and the state we project onto. The post-measurement bulk dual to Ac includes regions that were originally part of the entanglement wedge of A prior to measurement. This suggests that LPMs performed on a boundary subregion A teleport part of the bulk information originally encoded in A into the complementary region Ac. In semiclassical holography an arbitrary amount of bulk information can be teleported in this way, while in tensor network models the teleported information is upper-bounded by the amount of entanglement shared between A and Ac due to finite-N effects. When A is the union of two disjoint subregions, the measurement triggers an entangled/disentangled phase transition between the remaining two unmeasured subregions, corresponding to a connected/disconnected phase transition in the bulk description. Our results shed new light on the effects of measurement on the entanglement structure of holographic theories and give insight on how bulk information can be manipulated from the boundary theory. They could also represent a first step towards a holographic description of measurement-induced phase transitions.

AdS/BCFT with brane-localized scalar field

“…non-hermitian Hamiltonians or projection measurements. Note that if we perform projection measurements in the UV degrees of freedom, then the EOW brane should intersect with the AdS boundary as in the setups studied earlier [59,72]. Instead in our present construction, we expect non-unitary operations such as projections are acted on the IR degrees of freedom as the EOW brane is inserted in the interior.…”

“…. There are many other applications of the idea of AdS/BCFT, ranging from quantum many-body aspects of chaotic BCFTs [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73] and boundary renormalization group flows [74][75][76][77], to calculating quantum information measures [78][79][80][81][82][83][84][85][86] and building cosmological models [87][88][89][90][91]. The basic duality relations and their consistency of AdS/BCFT have also been analyzed in [92][93][94][95][96] and string theory realizations have also been studied in [97][98][99][100][101][102]…”

Holographic measurement and quantum teleportation in the SYK thermofield double

“…In particular, [14] initiated this work, showing that large portions of the bulk dual spacetime could indeed be destroyed (with the deleted region bounded by an end-of-theworld (ETW) brane) by postselecting a boundary subregion onto a specific class of states. This line of inquiry was furthered in [15], which gave a detailed account of this boundary measurement in vacuum AdS 3 /CFT 2 and in related tensor network models, and further showed how measurement could modify the bulk geometry and holographic dictionary via quantum teleportation. Of particular interest here, [15] showed that when measuring two disconnected boundary subregions, varying the measurement parameters could induce a phase transition corresponding to whether the remaining, unmeasured boundary regions were connected through the bulk time reflection symmetric slice or not.…”

“…This line of inquiry was furthered in [15], which gave a detailed account of this boundary measurement in vacuum AdS 3 /CFT 2 and in related tensor network models, and further showed how measurement could modify the bulk geometry and holographic dictionary via quantum teleportation. Of particular interest here, [15] showed that when measuring two disconnected boundary subregions, varying the measurement parameters could induce a phase transition corresponding to whether the remaining, unmeasured boundary regions were connected through the bulk time reflection symmetric slice or not. This bulk phase transition corresponded to an entangled/disentangled phase transition in the dual boundary theory.…”

Entanglement dynamics of the non-unitary holographic channel

“…This is especially true when it comes to studies involving conformal field theories. Some pioneering studies on projective measurements in two-dimensional conformal field theories (2d CFTs) can be found in [17][18][19].…”