Abstract We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterization of when it is consistent to treat a quantum subsystem classically in such a limit, namely: In any quantum state corresponding to a definite classical state in the classical limit, the reduced density matrix of the subsystem must be approximately proportional to a projection operator, and the projection operators for different classical subsystem states must obey an approximate mutual orthogonality condition. These are strong constraints on the entanglement structure of classical states. They generically give rise to fundamentally nonlocal classical degrees of freedom, which may nevertheless be accounted for using a completely local kinematical description, if one gauges this description in the right way. The mechanism we describe is very general, but for concreteness we exhibit a toy example involving three entangled spins at high angular momentum, and we also describe a significant group-theoretic generalization of this toy example. Finally, we give evidence that this phenomenon plays a role in the emergence of bulk diffeomorphism invariance in gravity.
Abstract We describe explicitly how entanglement between quantum mechanical subsystems can lead to emergent gauge symmetry in a classical limit. We first provide a precise characterization of when it is consistent to treat a quantum subsystem classically in such a limit, namely: In any quantum state corresponding to a definite classical state in the classical limit, the reduced density matrix of the subsystem must be approximately proportional to a projection operator, and the projection operators for different classical subsystem states must obey an approximate mutual orthogonality condition. These are strong constraints on the entanglement structure of classical states. They generically give rise to fundamentally nonlocal classical degrees of freedom, which may nevertheless be accounted for using a completely local kinematical description, if one gauges this description in the right way. The mechanism we describe is very general, but for concreteness we exhibit a toy example involving three entangled spins at high angular momentum, and we also describe a significant group-theoretic generalization of this toy example. Finally, we give evidence that this phenomenon plays a role in the emergence of bulk diffeomorphism invariance in gravity.
Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza-Klein proposal aims to recover gauge symmetries by means of dimensional reduction of higher-dimensional gravitational theories. Integrating both, gravitational and gauge degrees of freedom in 3+1 dimensions may be obtained upon dimensional reduction of higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with 5+1 and 9+1 dimensional spacetimes respectively, which are reduced to 3+1 dimensions upon singling out a preferred complex direction. In the latter case, this reduction is invariant under a residual SU(3)×SU(2)×U(1)/Z6 symmetry, the Standard Model gauge group. This motivates a picture in which spacetime emerges from the area law-contribution to the entanglement entropy, while gauge and matter degrees of freedom are due to area law-violating terms. We remark on a possible natural origin of the chirality of the weak force in the given construction. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields.
Abstract The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This, in turn, has recently led to applications to the study of entanglement in systems of identical particles. In the course of those investigations on entanglement and particle identity, an emergent gauge symmetry has been found by Balachandran, de Queiroz and Vaidya. In this letter we establish a novel connection between that gauge symmetry, entropy production and quantum operations. Thus, let A be a system described by a finite dimensional observable algebra and a mixed faithful state. Using the Gelfand–Naimark–Segal (GNS) representation we construct a canonical purification of , allowing us to embed A into a larger system C . Using Tomita–Takesaki theory, we obtain a subsystem decomposition of C into subsystems A and B , without making use of any tensor product structure. We identify a group of transformations that acts as a gauge group on A while at the same time giving rise to entropy increasing quantum operations on C . We provide physical means to simulate this gauge symmetry/quantum operation duality.
Entanglement is a hallmark of quantum theory, yet it alone does not capture the full extent of quantum complexity: some highly entangled states can still be classically simulated. Non-classical behavior also requires magic, the non-Clifford component that enables universal quantum computation. Here, we investigate whether the interplay between entanglement and magic-state resources constrains the structure of fundamental interactions. We study gluon-gluon and graviton-graviton scattering at tree level. We focus on the high-energy limit, where mass-dependent terms are negligible, and conformal symmetry is preserved. In this regime, all particles behave as massless degrees of freedom, allowing to isolate their transverse helicities as two-qubit states. We explicitly break gauge and general covariance by modifying the quartic vertices and analyzing the resulting generation of entanglement and magic. We find that imposing maximal entanglement (MaxEnt) alone does not uniquely recover gauge-invariant and diffeomorphism invariant interactions, but adding the condition of minimal, but nonzero, magic-state generation singles it out. Our results indicate that nature favors MaxEnt and low magic: maximal quantum correlations with limited non-Cliffordness, sufficient for universal quantum computing but close to classical simulability. This dual informational principle may underlie the emergence of gauge invariance in fundamental physics.
Entanglement is conventionally treated as an abstract property of tensor-product Hilbert spaces. We show instead that it can be realized as a global compatibility constraint in the internal gauge bundle of the vacuum, encoded by a locally pure-gauge field Ξ(x) acting only on internal degrees of freedom. This vacuum internal gauge symmetry (VIGS) yields a concrete, symmetry-based mechanism for quantum correlations that requires no nonlocal dynamics, introduces no new particles or forces, and leaves the Standard Model Lagrangian unchanged. Our main result is the Vacuum Internal Gauge Theorem, which demonstrates that: (i) all nontrivial global constraints induced by Ξ are confined to internal fibers; (ii) only internal degrees of freedom can become entangled; (iii) no information can be transmitted via the vacuum gauge structure; and (iv) gravitational degrees of freedom, having no internal fiber structure, cannot be entangled. Thus VIGS explains the empirical restriction of entanglement to internal DOFs and predicts the absence of gravitational entanglement, providing a gauge-theoretic foundation for quantum correlations within a strictly local spacetime.
The quantum nature of gravity remains experimentally unverified, despite recent proposals to probe it using tabletop experiments such as gravity-mediated entanglement schemes. In parallel, consistent formulations of classical--quantum dynamics have been developed as alternative descriptions of gravity, in which quantum matter interacts with a classical mediator assumed to be fundamentally classical. In this work, we show that classical--quantum dynamics arise generically as an effective description of fully quantum systems under decoherence, providing a bridge between fully quantum and classical--quantum dynamics. We derive the reduced dynamics, which are generically non-Markovian, using an explicit hidden model in which the mediator is coupled to unobserved environmental degrees of freedom. We identify a concrete criterion for when a classical--quantum interpretation is valid: the semi-Wigner operator associated with the mediator sector must remain positive semidefinite, which can be expressed as a positivity condition on nonlocal kernels governing the evolution. In the short-memory limit, the reduced evolution reproduces Markovian classical--quantum dynamics of Oppenheim and collaborators. Our results imply that a classical mediator can arise effectively from decohered quantum dynamics, so that experimental agreement with classical-quantum models does not uniquely determine whether the mediator is fundamentally classical.
Abstract Projected entangled pair states (PEPS) are very useful in the description of strongly correlated systems, partly because they allow encoding symmetries, either global or local (gauge), naturally. In recent years, PEPS with local symmetries have increasingly been used in the study of non-perturbative regimes of lattice gauge theories, most prominently as a way to construct variational ansatz states depending only on a small number of parameters and yet capturing the relevant physical properties. For the case of one-dimensional PEPS (matrix product states—MPS) a bidirectional connection was established between the internal structure of the tensor network, i.e. the mathematical properties of the constituent tensors, and the symmetry. In higher dimensions this has only been done for global symmetries, where in the local (gauge) case it is known only how to construct gauge-invariant states, but not what the symmetry implies on the internal structure of the PEPS. In the present work we complete this missing piece and study the internal structure of PEPS with a gauge symmetry. The PEPS we consider consist of matter and gauge field tensors placed on the vertices and edges, respectively, of arbitrary graphs.