出版者・発行元：arXiv  

We show that no EPR-like bipartite entanglement can be distilled from a tripartite Haar random state $|Ψ\rangle_{ABC}$ by local unitary rotations when each subsystem has fewer than half of the total qubits. Specifically, we derive an upper bound on the probability of sampling a state with EPR-like entanglement for a given EPR fidelity tolerance, showing a doubly-exponential suppression in the number of qubits. Our proof relies on a simple volume argument supplemented by an $ε$-net construction. We also discuss a physical interpretation in the AdS/CFT correspondence, indicating that a connected entanglement wedge does not necessarily imply bipartite entanglement as opposed to a previous belief.

DOI： 10.48550/ARXIV.2502.04437

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掲載種別：研究論文（学術雑誌）   出版者・発行元：arXiv  

In the AdS/CFT correspondence, direct scattering in the bulk may not have a local boundary analog. A nonlocal implementation on the boundary requires $O(1/G_N)$ mutual information. This statement is formalized by the connected wedge theorem, which can be proven using general relativity within AdS$_3$ but also by applying quantum information theory on the boundary, suggesting that the theorem applies to any holographic duality. We examine scattering within the static patch of asymptotically dS$_3$ spacetime, which is conjectured to be described by a quantum theory on the stretched horizon in static patch holography. We prove that causality on the horizon should be induced from null infinities $\mathcal{I}^{\pm}$ to maintain consistency with the theorem. Specifically, signals propagating in the static patch are associated with local operators at $\mathcal{I}^{\pm}$. Our results suggest a novel connection between static patch holography and the dS/CFT correspondence.

DOI： 10.1007/JHEP12(2024)199

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掲載種別：研究論文（学術雑誌）   出版者・発行元：arXiv  

The Ryu-Takayanagi formula predicts that two spatially separated boundary subsystems can have large mutual information if their entanglement wedge is connected in the bulk. However, the nature of this mysterious entanglement remains elusive. Here, we propose that i) there is no LO-distillable entanglement at the leading order in $1/G_{N}$ for holographic mixed states, suggesting the absence of bipartite entanglement, and ii) one-shot LOCC-distillable entanglement with holographic measurements is given by locally accessible information, which is related to the entanglement wedge cross section $E^W$ involving the (third) purifying system. In particular, we demonstrate that a connected wedge does not necessarily imply nonzero distillable entanglement with holographic measurements at the leading order. Thus, it is an example of NPT bound entanglement in one-shot holographic settings. Our proposals have parallel statements for Haar random states which may be of independent interest. We will also discuss potential physical mechanisms for subleading effects, namely i) holographic scattering, ii) traversable wormholes, and iii) Planck scale effects. Finally, we establish a holographic monogamy relation between distillable entanglement and entanglement of formation $E_F$ whose dual we propose is $E^W$.

DOI： 10.48550/ARXIV.2411.03426

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：arXiv  

Purification maps a mixed state to a pure state and a non-unitary evolution
into a unitary one by enlarging the Hilbert space. We link the operator
complexity of the density matrix to the state/operator complexity of purified
states using three purification schemes: time-independent, time-dependent, and
instantaneous purification. We propose inequalities among the operator and
state complexities of mixed states and their purifications, demonstrated with a
single qubit, two-qubit Werner states, and infinite-dimensional diagonal mixed
states. We find that the complexity of a vacuum evolving into a thermal state
equals the average number of Rindler particles created between left and right
Rindler wedges. Finally, for the thermofield double state evolving from zero to
finite temperature, we show that 1) the state complexity follows the Lloyd
bound, reminiscent of the quantum speed limit, and 2) the Krylov state/operator
complexities are subadditive in contrast to the holographic volume complexity.

DOI： 10.48550/ARXIV.2408.00826

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

Holography with branes and/or cutoff surfaces presents a promising approach
to studying quantum gravity beyond asymptotically anti-de Sitter spacetimes.
However, this generalized holography is known to face several inconsistencies,
including potential violations of causality and fundamental entropic
inequalities. In this work, we address these challenges by investigating the
bulk scattering process and its holographic realization. Specifically, we
propose that the information on a brane/cutoff surface $Q$ propagates according
to the induced light cones originating from a fictitious asymptotic boundary
behind $Q$, rather than the conventional ones originating from a point on $Q$.
Additionally, we establish the validity of the connected wedge theorem for
generalized holography with induced light cones. We also demonstrate that
entropic inequalities remain valid within the induced causal diamonds. While
the induced light cone seemingly permits superluminal signaling, we argue that
this causality violation can be an artifact of state preparation for radially
propagating excitations, rather than local operator excitations on $Q$.

DOI： 10.1007/jhep10(2023)104

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その他リンク： http://arxiv.org/pdf/2308.00739v1