Abstract
We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.
Highlights
Conjectured — based on analogies with black hole entropy via the AdS/CFT correspondence — that the amount of entanglement on the boundary of the spacetime is given by the area of certain extremal surfaces in the bulk [11]
We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state
The proposals we discuss in this paper are found in recent works [18,19,20,21] and talks [22,23,24] of van Raamsdonk, Swingle, Susskind, and Stanford: the core idea we explore is that the pattern of the entanglement of a state |ψ of a collection of degrees of freedom determines a dual bulk holographic spacetime via the principle of minimal complexity
Summary
The language and notation we use throughout this paper is influenced by that employed in the literature on the AdS/CFT correspondence; we summarise it here briefly to orient the reader. The unitary U diagonalising the boundary Hamiltonian H is the central object of interest here: its entangling structure determines an associated dual holographic bulk spacetime M The way this is done is by studying the quantum information complexity of U counting the number of nontrivial quantum gates required to implement U. (Here τ is the standard time coordinate for the boundary quantum system.) We discuss this idea in the second subsection These last two proposals may be regarded as a Wick-rotated “Euclidean approach” and “Lorentzian approach”, respectively, to the problem of building bulk holographic spacetimes associated with paths of unitaries
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