Whenever two very different areas of theoretical physics are found to be described by the same mathematical structures, it frequently leads to discover unexpected insights on both sides. This brief overview tries to explain why physicists in the areas of quantum gravity and string theory, especially those interested in the quantum structure of space-time are taking advantage from the knowledge of the structure of the quantum entanglement encoded in the wave-functions of quantum many body systems and tools such as tensor networks, initially devised by physicists in the area of quantum information. Quantum entanglement is the unique correlation allowed by quantum mechanics that Einstein famously called “spooky action at a distance.” Operationally speaking, entanglement means that information in an entangled quantum state is not stored in the individual parts at all, but only in the correlations among the parts. Entanglement is the major feature studied by quantum information science. It is the central concept underlying the ideas of quantum computers and quantum cryptography and lately it has also been successfully applied in classifying exotic phases of quantum matter. In addition, we have begun recently to understand how entanglement may be also the key to apprehend how space-time itself emerges from underlying microscopic quantum building blocks.

Indeed, any theory of quantum gravity faces strong conceptual problems due to the wild quantum fluctuations in the geometry of space-time that are supposed to free-run at the Planck scale. As one probes this shortest possible distance, space-time looks less and less like space-time. In words of physicist John Preskill, “it’s not really geometry anymore. It’s something else, an emergent thing that arises from something more fundamental.” What it has been recently proposed is that the fundamental threads from which a space-time fabric would emerge amount to the entanglement distribution between the degrees of freedom of an underlying and in some sense, more fundamental quantum theory.

In 2010 Mark Van Raamsdonk a string theorist at British Columbia, proposed a thought experiment to illustrate the critical role of entanglement in the formation of space-time. He found that disentangling the degrees of freedom of two contiguous regions of space-time is tantamount to disconnecting the regions altogether. In other words, space-time begins to tear itself apart, in much the same way that stretching a wad of gum by both ends yields a pinched-looking point in the center as the two halves move farther apart. Contrarily, by entangling distant degrees of freedom located at separate regions establishes spatial connections between them; as Van Raamsdonk says “if you wanted to build up a space-time, you’d want to start entangling qubits together in particular ways.”

Remarkably, these ideas have a natural arena to play with in the field of tensor network. A tensor network is a mathematical representation of the wave-function of a system made of a large number of interacting quantum constituents (qubits, electrons, spins…). As the data stored in the accounting department of a company can be understood as a reliable representation of the company’s state, a tensor network describes the state of the quantum many body system by, in some sense, providing a detailed account on how the quantum entanglement between the different constituents of the system is distributed.

There are many different types of tensor networks, but the kind of tensor networks much theorists are actually interested in is the MERA (multi-scale entanglement renormalization ansatz). Remarkably, it has been realized that the entanglement patterns within MERA can be represented as a diagram with the hyperbolic geometry intrinsic to the holographic proposals in string theory. This has led to the proposal that curved space-times may emerge quite naturally from entanglement in tensor networks via holography and that space-time, may be understood as a geometrical representation of this quantum information.

Within this background of ideas, questions related with, or relating the emergence of space-time symmetries (Poincarè, SUSY, conformal…) from lattice field theories, quantum and classical simulations for generic Renormalization Group flows and the emergence of geometry in the context of holography and tensor networks will be scrutinized by a miscellanea of researchers in the next years.


Javier Molina-Vilaplana.
Associate Professor. Universidad Politécnica de Cartagena.