Quantum error correction codes and absolutely maximally entangled states

In the last two decades, significant interest has been focused on the so-called AdS/CFT correspondence, which connects gravitational theories with conformal field theories. Even more recently, quantum information scientists have designed toy models of the AdS/CFT correspondence, in the form of tensor networks that give rise to quantum error correction codes. In particular, it was shown that an important feature of the AdS/CFT correspondence---the Ryu--Takayanagi formula that relates the entanglement entropy of the boundary of the network to the network geometry---holds in appropriately chosen tensor network codes.

These toy models heavily rely on an important class of multipartite quantum states, absolutely maximally entangled (AME) states, that are useful not only for quantum codes, but also in secret sharing schemes, and are of generic interest in entanglement theory. It was already known that AME states give rise to quantum error correction codes, and the AdS/CFT toy models are based on the concatenation of such codes.

In this talk, we will analyse the concatenation of quantum error correction codes based on AME states, and describe an algorithm for obtaining the explicit form of stabiliser generators and logical operators of the resulting codes. Using this algorithm, we will analyse the spread of quantum information in a specific AME-based tensor network code. We will calculate corrections to the Ryu--Takayanagi formula in the case of initial entanglement in the input quantum state, and find that in our specific case, AME states saturate a bound on these corrections. We conjecture that this saturation holds for generic tensor network codes, that is, AME states (when they exist) give the maximal value of the entanglement entropy of the boundary state.

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Zoom meeting details

Topic: Quantum Information and Quantum Computing Working Group
Time: November 12, 2020, 4:00 PM Warsaw

Join Zoom Meeting link (NEW LINK):
https://tinyurl.com/quantum-ctp

Meeting ID: 94552545103
Passcode: 323395

If you encounter any problems with connecting to the Zoom meeting, please email maciejewski@cft.edu.pl directly.

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