Abstract
Recent developments on holography and quantum information physics suggest that quantum information theory has come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still unknown. Here, we show that some concepts in quantum information theory have cosmological descriptions. Particularly, we show that the complexity of a tensor network can be regarded as a Fisher information measure (FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for f ( R ) gravity, whose FIM exhibits the same features of a recent proposed L n norm complexity.
Highlights
A milestone in the exploration of the unification of general relativity and quantum mechanics was the work of Bekenstein and Hawking on the area law of black hole entropy [1,2]
Correspondence holds for dS universe, we show that isometry in MERA can be viewed as a quantum gate which operates information bits and the dS universe may be understood as a MERA tensor network
The complexity of MERA which counts the number of operations on information bits is given by the on-shell action of the dS spacetime
Summary
A milestone in the exploration of the unification of general relativity and quantum mechanics was the work of Bekenstein and Hawking on the area law of black hole entropy [1,2]. This property suggests that log χ can be regarded as flux of entanglement flow in each leg and causal relation between tensors can be viewed as causal structure of the emergent spacetime [9,13]. The entanglement entropy is given by counting the number of legs on the causal cut Before discussing this MEAR/spacetime correspondence, let us first give a quick snapshot of tensor network in terms of the kinematic space of AdS3. We still lack knowledge of the correspondence between tensor network (or circuit) and gravity with general sources
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