Observer-Dependent Entanglement Wedge

• Observer-dependent entanglement wedge is a framework where the bulk region encoded in holography is determined by the observer's data, operations, and code subspace rather than a fixed boundary split.
• It encompasses several formulations, including dependencies on unknown couplings, localized modular flows, and distinctions between max- and min-entanglement wedges that affect black hole interior reconstruction.
• The approach underscores that observer actions and measurement choices directly influence causal accessibility and information flow within gravitational theories.

Observer-dependent entanglement wedge denotes a family of holographic constructions in which the bulk region regarded as encoded, reconstructible, or causally revealable is not fixed solely by a geometric boundary subregion, but depends on what data an observer has, which subsystem or screen is used, which code subspace is allowed, or which localized operation is performed. In the literature, this dependence appears in several technically distinct forms: the entanglement wedge of a reference system that stores unknown couplings, the causal revelation of a previously hidden “peninsula” by Connes cocycle flow, the distinction between max- and min-entanglement wedges for arbitrary gravitating regions, code-subspace-dependent reconstruction wedges, and screen-dependent wedges in de Sitter holography (Almheiri et al., 2021, Levine et al., 2020, Bousso et al., 2023, Akers et al., 2019).

1. Conceptual structure and principal variants

The standard AdS/CFT entanglement wedge is the bulk region reconstructible from a boundary region, determined semiclassically by a quantum extremal surface (QES). Several recent constructions replace the implicit assumption of a single, observer-independent reconstruction region by a more conditional notion. In one class of examples, the relevant condition is access to couplings or to a reference system that records them; in another, it is the observer’s ability to perform a localized modular-flow-like unitary; in another, it is whether one asks about inward reconstruction or outward irretrievability from a gravitating region; and in another, it is whether reconstruction must hold uniformly across an entire code subspace (Almheiri et al., 2021, Levine et al., 2020, Bousso et al., 2023, Akers et al., 2019).

Mechanism	What changes	Representative result
Unknown couplings stored in a reference	The reference can acquire an island behind the horizon	The reference wedge contains the black hole interior at late times
Localized cocycle flow in the causal wedge	The causal surface shifts by backreaction	The peninsula is brought into causal contact
Generalized wedge of a gravitating region	One distinguishes $e_{\rm max}(a)$ and $e_{\rm min}(a)$	$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$
Code-subspace reconstruction	Uniformly reconstructable region shrinks	$RW(A)$ can be much smaller than $EW(A)$

A persistent theme is that “observer dependence” does not always mean the same thing. In some papers it refers to different knowledge states, in some to different allowable operations, and in some to different subsystem definitions. This suggests that the term names a structural feature of bulk reconstruction rather than a single formalism.

2. Unknown couplings and the entanglement wedge of a reference

A direct realization appears in “The Entanglement Wedge of Unknown Couplings” (Almheiri et al., 2021). The setup considers a family of boundary theories labeled by couplings $\{\lambda_i\}$, with the couplings treated as quantum information stored in a reference system. The global state is prepared as

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$

and tracing out the reference gives

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$

The central claim is that the entanglement wedge of the reference is the bulk region most sensitive to the values of the couplings. If the couplings are known only statistically, the system’s entanglement wedge is smaller, and the missing region can appear as an island for the reference. For a pure global state, the system wedge and reference wedge are complementary. By contrast, for a classical pointer system there is no analogous island for the pointer, because the conditional matter entropy is positive and adding bulk region can only increase entropy.

In JT gravity coupled to a matter BCFT, the entanglement wedge is computed from the QES formula

$$S(\mathrm{sys}) = \min\left\{ \operatorname{ext}_I \left[ \sum_{\partial I}\frac{\phi(\partial I)}{4G} + S_m(I\cup \mathrm{sys}) \right] \right\},$$

while the conditional entropy with known couplings is

$$S(\mathrm{unknown}\mid \mathrm{known}) = \min\left\{ \operatorname{ext}_I \left[ \sum_{\partial I}\frac{\phi(\partial I)}{4G} + \langle S_{\mathrm{matter}}(I\cup \mathrm{unknown})\rangle \right] \right\}.$$

If one keeps only the trivial surface, the matter entropy of the reference grows with time because states with different boundary conditions become orthogonal under time evolution. In the free noncompact boson example, the matter entropy behaves as $e_{\rm min}(a)$0 at large $e_{\rm min}(a)$1, eventually competing with the black hole entropy and forcing the trivial saddle to fail. The late-time dominant saddle is then an island saddle, and the reference wedge includes the black hole interior.

For the peninsula computation, the dilaton profile is

$e_{\rm min}(a)$2

and the QES is located just outside the left horizon at

$e_{\rm min}(a)$3

The transition time depends on coupling uncertainty: broader uncertainty produces an earlier onset of the island. For a Gaussian distribution of couplings, the relevant time scale is described as

$e_{\rm min}(a)$4

The same paper relates the reference’s second Renyi entropy to a Loschmidt-echo-like diagnostic of chaos: $e_{\rm min}(a)$5 The naive disk saddle decays too fast and would violate unitarity; a replica wormhole saddle restores consistency and matches the island expectation. Numerical and analytical SYK evidence is presented for many marginal couplings and also for a single irrelevant coupling, suggesting that the interior remains sensitive even to irrelevant UV data. The paper’s final formulation is that the black hole interior is not only behind the horizon, but also behind uncertainty in the couplings.

3. Localized operations, causal revelation, and the peninsula

A different observer dependence appears in “Seeing the Entanglement Wedge” (Levine et al., 2020). For a boundary region $e_{\rm min}(a)$6, the paper distinguishes the causal wedge $e_{\rm min}(a)$7, the entanglement wedge $e_{\rm min}(a)$8, and the outermost extremal wedge $e_{\rm min}(a)$9. The key geometric region is the peninsula

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$0

the part of the outermost wedge lying outside the causal wedge.

The observer acts only in the causal wedge by a Connes cocycle unitary. For a region

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$1

the cocycle flow is

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$2

This unitary is localized to the algebra of the region in QFT, acts trivially on complementary spacelike observables, and in the vacuum/AdS case reduces componentwise to geometric modular flow. Its novelty is that the relative modular operator also produces a stress-tensor disturbance at the entangling surface.

In the perturbative regime, where the peninsula size scales as

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$3

the cocycle generates null energy shocks that shift the causal surface. The displacement obeys

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$4

so for $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$5,

$e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$6

leaving only a Planck-scale gap. In this sense, the same peninsula that was previously outside causal contact becomes visible to the boundary observer after a localized operation and its backreaction.

The paper emphasizes that the entanglement wedge is not changed abstractly; rather, the causal wedge is deformed until it reaches the previously hidden peninsula. This is an important distinction: the observer dependence lies in what becomes causally accessible after acting, not in a redefinition of the underlying extremal wedge itself. The construction is presented as a local and QFT-native generalization of the Gao–Jafferis–Wall mechanism.

4. Generalized wedges, information flow, and code-subspace dependence

“Holograms In Our World” extends entanglement wedges from AdS boundaries to arbitrary gravitating regions $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$7 (Bousso et al., 2023). The proposal defines two wedges rather than one: the max-entanglement wedge $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$8 and the min-entanglement wedge $e_{\rm min}(a)\supset e_{\rm max}(a)\supset a$9, satisfying

$RW(A)$0

The distinction is motivated by one-shot state-merging logic. $RW(A)$1 is the largest wedge consistent with reconstructing information into $RW(A)$2, whereas $RW(A)$3 is the smallest wedge such that all information outside it can flow outward from $RW(A)$4.

The information-theoretic interpretation is explicit. All information outside $RW(A)$5 in $RW(A)$6 can flow inward toward $RW(A)$7, while all information outside $RW(A)$8 can flow outward away from $RW(A)$9. The capacity of a bottleneck surface $EW(A)$0 is controlled by

$EW(A)$1

The generalized entropies of appropriate wedges obey strong subadditivity, and the wedges satisfy a no-cloning relation for suitably independent regions. The paper stresses that $EW(A)$2 and $EW(A)$3 can differ already at the classical level, so the observer dependence here is not merely a quantum correction.

A complementary limitation appears in “Large Breakdowns of Entanglement Wedge Reconstruction” (Akers et al., 2019). There the relevant object is the reconstruction wedge

$EW(A)$4

the intersection of entanglement wedges over all states in the code subspace. This region can be much smaller than the entanglement wedge of any particular pure state, even when backreaction is small. Near entanglement phase transitions and in large-energy but low-energy-density dustball examples, $EW(A)$5 can differ macroscopically from $EW(A)$6. The operative criterion is the generalized-entropy competition

$EW(A)$7

or schematically

$EW(A)$8

In qubit models this becomes

$EW(A)$9

Taken together, these constructions show two different forms of observer dependence. In generalized wedges, the question is which information-theoretic task is being posed for a gravitating region. In reconstruction wedges, the question is what an observer can reconstruct uniformly given only code-subspace knowledge rather than full state knowledge.

5. Observer rules, hollowing, and algebraic island constructions

A more explicit observer-based reformulation appears in “Subregion observer rules from generalized entanglement wedges” (Bozanic et al., 26 Jun 2026). The paper argues that the Colorado observer-promotion rules and the Kaya–Rath–Ritchie hollowing rules are exactly equivalent tensor-network operations: the tensors in a chosen bulk subregion $\{\lambda_i\}$0 are removed, the subregion is left as effective output data, and dangling legs remain across $\{\lambda_i\}$1. The resulting replica computation treats the bulk subregion as boundary-like data. For fixed-geometry states $\{\lambda_i\}$2,

$\{\lambda_i\}$3

and the entropy takes the generalized-wedge form

$\{\lambda_i\}$4

If one does not enforce cyclic gluing on $\{\lambda_i\}$5, the dominant contribution is trivial,

$\{\lambda_i\}$6

The generalized entanglement wedge therefore arises precisely because the observer subregion is treated specially in the replica construction.

In JT gravity, the same paper uses the rule $\{\lambda_i\}$7 and derives a fundamental-Hilbert-space scaling

$\{\lambda_i\}$8

This is presented as the path-integral counterpart of the observer-dependent area factor in tensor-network models.

“Algebras, Entanglement Islands, and Observers” develops an operator-algebraic realization in the island model (Geng et al., 13 Jun 2025). In an asymptotically AdS gravitational region coupled to a non-gravitational bath, the island prescription is

$\{\lambda_i\}$9

The paper identifies the required “observer” with a Goldstone vector field $$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$0 arising from spontaneous breaking of AdS diffeomorphisms by the bath coupling. Island operators are dressed to this observer as

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$1

Assuming the geometric modular flow conjecture, the algebra of dressed island operators extends by a crossed product with the modular flow and becomes a Type II$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$2 von Neumann factor. The entropy of semiclassical states then takes the generalized-entropy form

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$3

These constructions make the observer dependence highly concrete: the observer is not merely interpretive, but enters the replica rules, the Hilbert-space bookkeeping, and the operator dressing needed for gravitational subregions.

6. de Sitter screens, generalized Rindler wedges, and future–past wedges

Observer-dependent wedge structure also appears outside the standard AdS setting. In “de Sitter Connectivity from Holographic Entanglement,” two antipodal static observers are associated with holographic screens $$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$4 and $$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$5 on stretched horizons (Franken, 2024). For the full two-screen system,

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$6

the entropy is

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$7

and the entanglement wedge is

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$8

Thus the joint system reconstructs not only the two static patches but also the exterior region connecting them. For a single screen, however, there is a phase transition between two competing exterior QESs,

$$|\Psi\rangle_{\mathrm{sys}+\mathrm{ref}} = \sum_{\lambda}\sqrt{P(\lambda)}\,|\psi;\lambda\rangle_{\mathrm{sys}}\otimes|\lambda\rangle_{\mathrm{ref}},$$9

with transition at $$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$0. Correspondingly,

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$1

The encoding of the exterior region can therefore transfer from one screen to the other.

“Generalized Rindler Wedge and Holographic Observer Concordance” defines gravitational subsystems directly from accelerating observers (Ju et al., 2023). A region is admissible only if its boundary is Rindler-convex, meaning that the normal null geodesics outside its boundary never intersect to form caustics. The accessible spacetime region is the generalized Rindler wedge, denoted $$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$2. Its entropy is derived by a replica argument as

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$3

The paper stresses that GRW is not generally the same as the entanglement wedge: the causal wedge is the outermost GRW for a given boundary spatial region in AdS vacuum, whereas the entanglement wedge is generally deeper and usually not a GRW.

A different de Sitter analogue appears in “On de Sitter future-past extremal surfaces and the ‘entanglement wedge’” (Narayan, 2020). There the basic objects are codimension-2 future-past extremal surfaces connecting a subregion of $$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$4 to an equivalent subregion of $$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$5. In $$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$6, the turning points are bounded by a limiting surface at

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$7

The union of the resulting family of codimension-2 surfaces across equivalent boundary slices defines an effective codimension-1 envelope, interpreted as a de Sitter analogue of the entanglement wedge. For multiple disjoint subregions, the construction gives

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$8

and saturates strong subadditivity at leading order.

7. Related diagnostics, precursors, and recurrent misconceptions

Several adjacent developments sharpen the meaning of observer dependence without always introducing a formal observer-dependent wedge. “Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories” computes reflected entropy,

$$\rho_{\mathrm{sys}} = \sum_{\lambda}P(\lambda)\rho_{\psi}(\lambda) = \langle \rho_\psi\rangle_{\lambda}.$$9

in time-dependent holographic CFT states produced by a local operator quench (Kusuki et al., 2019). The paper explicitly states that it does not formulate a formal observer-dependent entanglement wedge, but it argues that the effective meaning of the wedge depends on the dynamical state and on which correlations are accessible to a given subregion decomposition. Outside the active crossing window, reflected entropy can remain nonzero while mutual information does not capture the same behavior, indicating that classical correlations play a significant role in subregion/subregion duality.

A more distant precursor is “Observer dependent entanglement” (Alsing et al., 2012). That work does not discuss an entanglement wedge in the holographic sense, but it does establish the core relativistic mechanism behind observer dependence: different observers define different subsystem decompositions because particle notions depend on motion and geometry. Uniform acceleration leads to Rindler wedges and tracing over an inaccessible region,

$$S(\mathrm{sys}) = \min\left\{ \operatorname{ext}_I \left[ \sum_{\partial I}\frac{\phi(\partial I)}{4G} + S_m(I\cup \mathrm{sys}) \right] \right\},$$0

with Unruh temperature

$$S(\mathrm{sys}) = \min\left\{ \operatorname{ext}_I \left[ \sum_{\partial I}\frac{\phi(\partial I)}{4G} + S_m(I\cup \mathrm{sys}) \right] \right\},$$1

This is a precursor in which horizons, accessible regions, and reduced states are already observer dependent, although without the later holographic wedge formalism.

Several misconceptions recur across the subject. First, observer dependence does not always mean that the extremal wedge itself changes: in the cocycle construction, the abstract entanglement wedge remains fixed while the causal wedge moves by backreaction (Levine et al., 2020). Second, not every record of hidden data behaves like an entangled reference: a classical pointer does not generically develop islands, whereas an entangled reference can (Almheiri et al., 2021). Third, generalized observer-based wedges need not coincide with standard entanglement wedges: GRW is explicitly broader than the causal-wedge family but usually smaller than the entanglement wedge, and the de Sitter bilayer prescription is argued to be consistent while the monolayer proposal is argued to be inconsistent (Ju et al., 2023, Franken, 2024). Finally, entanglement-wedge reconstruction is not automatically uniform across a code subspace; the reconstruction wedge can be much smaller than the state-by-state entanglement wedge (Akers et al., 2019).

Taken together, these results support a common conclusion: the bulk region assigned to a subsystem is often conditional on knowledge, algebra, screen choice, operational capability, or code subspace. The observer-dependent entanglement wedge is therefore best understood not as a single definition, but as a set of closely related mechanisms by which holographic reconstruction acquires an explicitly conditional character.