# Families of Perfect Tensors

@article{Geng2022FamiliesOP, title={Families of Perfect Tensors}, author={Runshi Geng}, journal={ArXiv}, year={2022}, volume={abs/2211.15776} }

Perfect tensors are the tensors corresponding to the absolutely maximally entangled states, a special type of quantum states of interest in quantum information theory. We establish a method to compute parameterized families of perfect tensors in ( C d ) ⊗ 4 using exponential maps from Lie theory. With this method, we ﬁnd explicit examples of non-classical perfect tensors in ( C 3 ) ⊗ 4 . In particular, we answer an open question posted by ˙Zyczkowski et al.

## References

SHOWING 1-10 OF 18 REFERENCES

### Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence

- Computer Science
- 2015

That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].

### Absolutely maximally entangled states, quantum-maximum-distance-separable codes, and quantum repeaters

- Computer SciencePhysical Review A
- 2021

A generic reduction-friendly form is introduced for the generator set of the stabilizer representation of an AME state, from which the stabilized form for children codes, all QMDS, can be obtained.

### Thirty-six Entangled Officers of Euler: Quantum Solution to a Classically Impossible Problem.

- PhysicsPhysical review letters
- 2022

The negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers…

### 9 × 4 = 6 × 6: Understanding the Quantum Solution to Euler’s Problem of 36 Officers

- PhysicsJournal of Physics: Conference Series
- 2023

The famous combinatorial problem of Euler concerns an arrangement of 36 officers from six different regiments in a 6×6 square array. Each regiment consists of six officers each belonging to one of…

### Mixed-state entanglement and quantum error correction.

- Computer SciencePhysical review. A, Atomic, molecular, and optical physics
- 1996

It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.

### Entangling power of permutations

- Mathematics
- 2005

The notion of entangling power of unitary matrices was introduced by Zanardi et al., [Phys. Rev. A 62, 030301 (2000)]. We study the entangling power of permutations, given in terms of a combinatorial…

### Handbook of Combinatorial Designs

- Mathematics
- 2006

PREFACE INTRODUCTION NEW! Opening the Door NEW! Design Theory: Antiquity to 1950 BLOCK DESIGNS 2-(v, k, ?) Designs of Small Order NEW! Triple Systems BIBDs with Small Block Size t-Designs with t = 3…

### Absolute maximal entanglement and quantum secret sharing

- Physics
- 2012

We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for…

### There exist and only exist five irreducible components of P(4, 3) that are smooth at Φ, which are: exp Φ (span R {g j | 1 ≤ j ≤ 9}), exp Φ (span R {e i , e i+1 , e i+2 , f i , f i+1

- Conjuncture 13