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Baby universe as logical qubits: information recovery in random encoding

Takato Mori, Beni Yoshida

Abstract

We revisit whether a semiclassical baby universe in AdS/CFT necessarily possess a trivial one-dimensional Hilbert space or may instead carry a large entropy. Recent results on Haar random encoding suggest a breakdown of complementary recovery, in which no logical operators can be reconstructed from individual bipartite subsystems. Motivated by this, we propose an interpretation where a baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, assuming pseudorandom dynamics in holographic CFTs. We then analyze two conceptual puzzles: an apparent cloning of baby-universe microstates and its eventual fate at the singularity. Both puzzles are avoided because no single boundary observer can access the baby-universe degrees of freedom, be it classical or quantum, reflecting an emergent form of complementarity due to the structure of random encoding. In this interpretation, observers arise naturally: the same heavy operator that prepares the baby-universe geometry also serves as observer-like degrees of freedom that define an observer-dependent baby-universe microstate.

Baby universe as logical qubits: information recovery in random encoding

Abstract

We revisit whether a semiclassical baby universe in AdS/CFT necessarily possess a trivial one-dimensional Hilbert space or may instead carry a large entropy. Recent results on Haar random encoding suggest a breakdown of complementary recovery, in which no logical operators can be reconstructed from individual bipartite subsystems. Motivated by this, we propose an interpretation where a baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, assuming pseudorandom dynamics in holographic CFTs. We then analyze two conceptual puzzles: an apparent cloning of baby-universe microstates and its eventual fate at the singularity. Both puzzles are avoided because no single boundary observer can access the baby-universe degrees of freedom, be it classical or quantum, reflecting an emergent form of complementarity due to the structure of random encoding. In this interpretation, observers arise naturally: the same heavy operator that prepares the baby-universe geometry also serves as observer-like degrees of freedom that define an observer-dependent baby-universe microstate.

Paper Structure

This paper contains 9 sections, 4 theorems, 43 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Tripartite random state
  3. Toy baby universe: Haar random encoding
  4. Baby universe in CFTs
  5. Bulk picture: cloning puzzle and singularity
  6. Outlook
  7. Tripartite random entanglement
  8. Local unitaries
  9. Logical operators

Key Result

Theorem 1

The probability of sampling a quantum state $|\psi_{ABC}\rangle$ with locally distillable EPR pairs are exponentially suppressed with respect to $d$: where $\alpha>0$ is some constant and $E_{D}$ denotes the number of EPR pairs distillable by local unitaries or operations.

Figures (4)

  • Figure 1: A baby universe appears as an effectively closed region outside entanglement wedges of two individual boundaries.
  • Figure 2: Semiclassical baby universe.
  • Figure 3: A cloning puzzle at the $t=0$ slice. A copy of the bulk baby-universe state $|\psi_c^{(i)}\rangle$ can be reconstructed from two AdS regions $a,b$.
  • Figure 4: A singularity puzzle. The reference system $C$ is initially entangled with heavy operators $O^{(i)}$ which eventually fall into a singularity. Entanglement between $c$ and $C$ appears to be lost.

Theorems & Definitions (4)

  • Theorem 1: informal
  • Theorem 2: informal
  • Theorem 3
  • Theorem 4