# Polarization of Quantum Channels Using Clifford-Based Channel Combining

@article{Dupuis2019PolarizationOQ,
title={Polarization of Quantum Channels Using Clifford-Based Channel Combining},
author={Fr{\'e}d{\'e}ric Dupuis and Ashutosh Goswami and Mehdi Mhalla and Valentin Savin},
journal={IEEE Transactions on Information Theory},
year={2019},
volume={67},
pages={2857-2877}
}
• Published 9 April 2019
• Computer Science
• IEEE Transactions on Information Theory
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate randomly chosen from the Clifford group is used to combine two single-qubit channels. The inputs to the synthesized bad channels are frozen by preshared EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that…
3 Citations

## Figures from this paper

### Multilevel polarization for quantum Channels

• Physics
Quantum Inf. Comput.
• 2021
This work considers the quantum polar code construction using the same channel combining and splitting procedure as in [3] but with a fixed two-qubit Clifford unitary and gives an upper bound on the number of preshared EPR pairs, which is an equality in the case of quantum erasure channel.

### Quantum Polarization of Qudit Channels

• Computer Science
2021 IEEE International Symposium on Information Theory (ISIT)
• 2021
A generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel and showing how to decode the proposed quantum polar code on Pauli qudit channels.

### Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit

• Computer Science
• 2022
This paper explores a new approach to fault-tolerant quantum computing, relying on quantum polar codes of Calderbank-Shor-Steane type, encoding one logical qubit, and shows that a subfamily of Q1 codes is equivalent to the well-known family of Shor codes.

## References

SHOWING 1-10 OF 27 REFERENCES

### Polarization for arbitrary discrete memoryless channels

• Computer Science
2009 IEEE Information Theory Workshop
• 2009
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime

### Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels

• E. Arıkan
• Computer Science
IEEE Transactions on Information Theory
• 2009
The paper proves that, given any B-DMC W with I(W) > 0 and any target rate R< I( W) there exists a sequence of polar codes {Cfrn;nges1} such that Cfrn has block-length N=2n, rate ges R, and probability of block error under successive cancellation decoding bounded as Pe(N,R) les O(N-1/4) independently of the code rate.

### Probability Inequalities for Sums of Bounded Random Variables

• Mathematics
• 1994
If S is a random variable with finite rnean and variance, the Bienayme-Chebyshev inequality states that for x > 0, \Pr \left[ {\left| {S - ES} \right| \geqslant x{{{(\operatorname{var}

### Continuity of quantum conditional information

• Mathematics
• 2003
We prove continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This

### Real and Abstract Analysis: A Modern Treatment of the Theory of Functions of a Real Variable

• Mathematics
• 1965
This book is first of all designed as a text for the course usually called "theory of functions of a real variable," and has presented very general and complete versions of a number of important theorems and constructions.

### Efficient quantum channel coding scheme requiring no preshared entanglement

• Computer Science
2013 IEEE International Symposium on Information Theory
• 2013
An explicit entanglement distillation scheme is constructed which achieves the coherent information when used to send quantum information over a noisy quantum channel and how the scheme can be used for secret key distillation and private channel coding is discussed.

### Belief propagation decoding of quantum channels by passing quantum messages

• J. Renes
• Computer Science
2017 IEEE International Symposium on Information Theory (ISIT)
• 2017
This work constructs the first BP algorithm which passes quantum messages on the factor graph and is capable of decoding the classical–quantum channel with pure state outputs and gives explicit decoding circuits whose number of gates is quadratic in the code length.

### Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints

Under some regularity assumptions on the Hamiltonian, the Gibbs entropy at the given energy roughly takes the role of the Hilbert space dimension in the finite-dimensional Fannes inequality.

### Catalytic Quantum Error Correction

• Computer Science
IEEE Transactions on Information Theory
• 2014
The theory of entanglement-assisted quantum error-correcting (EAQEC) codes is developed, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to presharedEntanglement, which greatly simplifies their construction.

### Correcting Quantum Errors with Entanglement

• Computer Science, Physics
Science
• 2006
The entanglement-assisted quantum codes described do not require the dual-containing constraint necessary for standard quantum error–correcting codes, thus allowing us to “quantize” all of classical linear coding theory.