Abstract:Information-theoretic ideas have provided numerous insights in the progress of fundamental physics, especially in our pursuit of quantum gravity. In particular, the holographic entanglement entropy is a very useful tool in studying AdS/CFT, and its efficacy is manifested in the recent black hole page curve calculation. On the other hand, the one-shot information-theoretic entropies, such as the smooth min/max-entropies, are less discussed in AdS/CFT. They are however more fundamental entropy measures from the … Show more
“…In this picture, rather 1 Let us emphasize the proviso: this is only true for appropriate holographic states. As shown in [11] (see also [15]), there are some semiclassical holographic states -i.e. simple states of bulk quantum matter on fixed semiclassical geometric backgrounds -for which (1) does not apply for any bulk region b, even as a leading order semiclassical approximation.…”
Section: Background and Motivationmentioning
confidence: 87%
“…[1] for others. 15 Theorem 3.1 (Formulations of exact state-independent QEC). Let V : H code → H B ⊗ H B be an isometry between finite-dimensional Hilbert spaces.…”
“…16 We will return to it when we talk about state-specific reconstruction. 15 To see the equivalence of the conditions in Theorem 3.1 below and those in Theorem 3.1 of [1], note that Condition 3 below is manifestly equivalent to the Hermitian and anti-Hermitian parts of Condition 2 of Theorem 3.1 of [1]. 16 See e.g.…”
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow[1]; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining ``areas'' associated to arbitrary logical subsystems, and argue that this definition is ``functionally unique.'' We also formalize a definition of bulk reconstruction that we call ``state-specific product unitary’’ reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases.
Our results extend to approximate codes, and even to the ``non-isometric codes'' that seem to describe the interior of a black hole at late times.
“…In this picture, rather 1 Let us emphasize the proviso: this is only true for appropriate holographic states. As shown in [11] (see also [15]), there are some semiclassical holographic states -i.e. simple states of bulk quantum matter on fixed semiclassical geometric backgrounds -for which (1) does not apply for any bulk region b, even as a leading order semiclassical approximation.…”
Section: Background and Motivationmentioning
confidence: 87%
“…[1] for others. 15 Theorem 3.1 (Formulations of exact state-independent QEC). Let V : H code → H B ⊗ H B be an isometry between finite-dimensional Hilbert spaces.…”
“…16 We will return to it when we talk about state-specific reconstruction. 15 To see the equivalence of the conditions in Theorem 3.1 below and those in Theorem 3.1 of [1], note that Condition 3 below is manifestly equivalent to the Hermitian and anti-Hermitian parts of Condition 2 of Theorem 3.1 of [1]. 16 See e.g.…”
We show that complementary state-specific reconstruction of logical (bulk) operators is equivalent to the existence of a quantum minimal surface prescription for physical (boundary) entropies. This significantly generalizes both sides of an equivalence previously shown by Harlow[1]; in particular, we do not require the entanglement wedge to be the same for all states in the code space. In developing this theorem, we construct an emergent bulk geometry for general quantum codes, defining ``areas'' associated to arbitrary logical subsystems, and argue that this definition is ``functionally unique.'' We also formalize a definition of bulk reconstruction that we call ``state-specific product unitary’’ reconstruction. This definition captures the quantum error correction (QEC) properties present in holographic codes and has potential independent interest as a very broad generalization of QEC; it includes most traditional versions of QEC as special cases.
Our results extend to approximate codes, and even to the ``non-isometric codes'' that seem to describe the interior of a black hole at late times.
“…We will assume throughout that the max-QFC and (von Neumann) QFC both hold. 17 Let us motivate these consistency conditions. The first is that in certain cases, the max-EW and min-EW should coincide, and in such cases should equal the QES region.…”
Section: Propertiesmentioning
confidence: 99%
“…See also[17][18][19] for additional discussion 3. One also has access to unlimited classical bits (or more generally zero-bits) containing information about A 4.…”
Following the work of [J. High Energy Phys. 04, 062 (2021)], we define a generally covariant max-entanglement wedge of a boundary region B, which we conjecture to be the bulk region reconstructible from B. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on B. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.
The JLMS formula relates the bulk and boundary relative entropies and is fundamental to the holographic dictionary, providing justification for entanglement wedge reconstruction. We revisit the replica trick for relative entropy and find corrections to the JLMS formula in a variety of scenarios, even after accounting for effects of quantum extremality. We analyze the problem in the PSSY model, a model of Jackiw-Teitelboim gravity coupled to end-of-the-world branes. We find non-perturbative (in G) corrections that are always present, arising from subdominant replica wormhole gravitational saddles that indicate the approximate error-correcting nature of AdS/CFT. Near entanglement phase transitions, these saddles can get enhanced to large corrections. We find O (G−1/2) corrections arising from area fluctuations and O (G−1) corrections from incompressible bulk quantum states. Lastly, we find our most surprising result, an infinite violation of the JLMS formula after the Page time arising from a rank deficiency in the bulk entanglement spectrum. We discuss similar calculations in tensor networks and comment on the implications for bulk reconstruction.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.