We show that in the operational setting of a two-agent, local operations, classical communication (LOCC) protocol, Alice and Bob cannot operationally distinguish monogamous entanglement from a topological identification of points in their respective local spacetimes, i.e. that ER = EPR can be recovered as an operational theorem. Our construction immediately implies that in this operational setting, the local topology of spacetime is observer-relative. It also provides a simple demonstration of the non-traversability of ER bridges. As our construction does not depend on an embedding geometry, it generalizes previous geometric approaches to ER = EPR.
We show that in the operational setting of a two-agent, local operations, classical communication (LOCC) protocol, Alice and Bob cannot operationally distinguish monogamous entanglement from a topological identification of points in their respective local spacetimes, i.e. that ER = EPR can be recovered as an operational theorem. Our construction immediately implies that in this operational setting, the local topology of spacetime is observer-relative. It also provides a simple demonstration of the non-traversability of ER bridges. As our construction does not depend on an embedding geometry, it generalizes previous geometric approaches to ER = EPR.
We point out a necessary condition that a quantum measurement can be implemented by the class of protocols known as Local Operations and Classical Communication, or LOCC, including in the limit of an infinite number of rounds. A generalization of this condition is then proven to hold for any measurement that is in the closure of that set, LOCCˉ. This generalization unifies, extends, and provides a geometric justification for previously known results on LOCCˉ, reproducing their consequences with regard to practical applications. We have also used our condition to answer a variety of long-standing, unsolved problems, including for distinguishability of certain sets of states by LOCC. These include various classes of unextendible product bases, for which we prove they cannot be distinguished by LOCC even when infinite resources are available and vanishing error is allowed.
Abstract Topological quantum field theories (TQFTs) provide a general, minimal‐assumption language for describing quantum‐state preparation and measurement. They therefore provide a general language in which to express multi‐agent communication protocols, e.g., local operations, classical communication (LOCC) protocols. Here, LOCC protocols are constructed using TQFT and it is shown that LOCC protocols generically induce quantum error‐correcting codes (QECCs). Using multi‐observer scenarios described by quantum Darwinism and Bell/EPR experiments as examples, it is shown how these LOCC‐induced QECCs effectively convert entanglement into classical redundancy. In the accompanying Part II, it is shown that such QECCs can be regarded as implementing, or inducing the emergence of, spacetimes on the boundaries between interacting systems. The connection between inter‐agent communication and spacetime using BF and Chern‐Simons theories, and then using topological M‐theory is investigated.
We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way local operations and classical communication (LOCC) where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N ⩽ d maximally entangled states in d ⊗ d for d = 4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly, for d = 5,6, our examples consist of four and five states, respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.
Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories.
This preprint offers a minimal, background-independent logical re-reading of the ER=EPR conjecture using the Logical Language (LL) of standard quantum mechanics. ER=EPR links quantum entanglement to geometric connections (Einstein–Rosen bridges) in emergent spacetime, with standard arguments relying on AdS/CFT and the Ryu–Takayanagi formula. LL strictly follows textbook QM and classical logic, defining physical existence solely by in-principle distinguishability (a detector). Undefined classical local spacetime variables across regions thus lack independent reality. Consistency then requires stronger-than-classical correlations to maintain connectivity, yielding the simple relation: the closer two points, the stronger the correlation. This captures ER=EPR’s core intuition (entanglement as geometric proximity) with far fewer assumptions—no duality, no holographic background, no new postulates—using only standard QM. The note recaps LL (definitional existence, operating setups), illustrates via double-slit and EPR examples, and derives the correlation–distance link from two premises (Consistency and Definitional Existence).
This paper discusses ER = EPR, the hypothesis of Susskind and Maldacena that entangled black holes are connected by an Einstein-Rosen bridge, and that more generally, quantum entanglement is accompanied by topological connectivity. Given a background space and a quantum tensor network, we describe how to construct a new topological space, that welds the network and the background space together. This construction embodies the principle that quantum entanglement and topological connectivity are intimately related.