科学研究

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【Seminar】Entropy in Invariant Subspace

Speaker


Dr. Youning Li 

Tsinghua University                                                       

 

Host


Prof. Ying Li(李颖)


Date&Time


2018-09-26   10:00~11:00 AM


Venue


C305 Conference Room, 3th Floor


Abstract 


Invariant tensors are states in the SU(2) tensor product representation that are invariant under the SU(2) action. They play an important role in the study of loop quantum gravity, particularly the structure of Spin-Networks, which represents the quantization of geometry. Perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Perfect tensors have been employed to construct the Tensor Network as a Conformal Field Theory (CFT) ground state, which realizes the AdS/CFT correspondence. In terms of quantum error-correcting codes, a perfect tensor is a code with large code distance that is half of the system size. A constant weight subspace is natural immunity to the corresponding collective decoherence error. Therefore, an invariant subspace, in which the weight of all states is 0, is natural immunity to different kinds of collective decoherence error. In this talk, we are going to show that, the combinatorial properties of the constant weight condition impose strong constraints on the reduced density matrices for any vector in the constant weight subspace, and hence limit the possibility of the entanglement structures. As a result, no perfect tensor exists in invariant subspace, but their entanglement entropy is very close to a perfect tensor. The average deficit in invariant subspace can be even smaller than 1/2, which is the average deficit for the whole Hilbert space.


About the Speaker


Youning Li received his bachelor degree from Tsinghua University in 2007. After that he earned his PhD Degree from Tsinghua University in 2013. Dr.Li’s research focuses on the Representation theory and its application in physics, Exact solvable quantum system and Entanglement in quantum information. .


All interested are welcome!