scholarly journals Improved quantum hypercontractivity inequality for the qubit depolarizing channel

2021 ◽  
Vol 62 (12) ◽  
pp. 122201
Author(s):  
Salman Beigi
Keyword(s):  
Depolarizing Channel

scholarly journals Degenerate Quantum LDPC Codes With Good Finite Length Performance

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 585
Author(s):  
Pavel Panteleev ◽  
Gleb Kalachev
Keyword(s):  
Minimum Distance ◽  
Belief Propagation ◽  
Fault Tolerant ◽  
Large Family ◽  
Parity Check ◽  
Product Codes ◽  
Medium Length ◽  
Surface Code ◽  
Depolarizing Channel ◽  
Better Than

We study the performance of medium-length quantum LDPC (QLDPC) codes in the depolarizing channel. Only degenerate codes with the maximal stabilizer weight much smaller than their minimum distance are considered. It is shown that with the help of OSD-like post-processing the performance of the standard belief propagation (BP) decoder on many QLDPC codes can be improved by several orders of magnitude. Using this new BP-OSD decoder we study the performance of several known classes of degenerate QLDPC codes including hypergraph product codes, hyperbicycle codes, homological product codes, and Haah's cubic codes. We also construct several interesting examples of short generalized bicycle codes. Some of them have an additional property that their syndromes are protected by small BCH codes, which may be useful for the fault-tolerant syndrome measurement. We also propose a new large family of QLDPC codes that contains the class of hypergraph product codes, where one of the used parity-check matrices is square. It is shown that in some cases such codes have better performance than hypergraph product codes. Finally, we demonstrate that the performance of the proposed BP-OSD decoder for some of the constructed codes is better than for a relatively large surface code decoded by a near-optimal decoder.

scholarly journals Quantum Flags and New Bounds on the Quantum Capacity of the Depolarizing Channel

2020 ◽  
Vol 125 (2) ◽  
Author(s):  
Marco Fanizza ◽  
Farzad Kianvash ◽  
Vittorio Giovannetti
Keyword(s):  
Quantum Capacity ◽  
Depolarizing Channel

ENTANGLEMENT-ASSISTED CLASSICAL CAPACITIES OF SOME SINGLE QUBIT QUANTUM NOISY CHANNELS

2002 ◽  
Vol 16 (12) ◽  
pp. 441-448 ◽  
Author(s):  
XIAN-TING LIANG ◽  
HONG-YI FAN
Keyword(s):  
Noisy Channels ◽  
Single Qubit ◽  
Phase Damping ◽  
Analytical Results ◽  
Bit Flip ◽  
Depolarizing Channel ◽  
Quantum Noisy Channels

In this paper, we calculate the entanglement-assisted classical capacities of the depolarizing channel, the phase damping channel, the phase flip channel, the bit flip channel, the bit-phase flip channel, the two-Pauli channel and the amplitude channel, and discuss the analytical results obtained. The Stokes papametrization representation of a qubit and the characteristic of unitary covariance of some quantum noisy channels are used in the calculations.

scholarly journals INVESTIGATION OF QUANTUM ROULETTE

2009 ◽  
Vol 07 (03) ◽  
pp. 615-626 ◽  
Author(s):  
S. SALIMI ◽  
M. M. SOLTANZADEH
Keyword(s):  
Symmetric Group ◽  
Quantum Game ◽  
Permutation Matrices ◽  
Fourier Matrix ◽  
Depolarizing Channel ◽  
General Method ◽  
Quantum Roulette

In this paper, by using permutation matrices as a representation of symmetric group SN and Fourier matrix, we investigate quantum roulette with an arbitrary N-state. This strategy, which we introduce, is a general method that allows us to solve quantum game for an arbitrary N-state. We consider the interaction between the system and its environment and study the effect of the depolarizing channel on this strategy. Finally, as an example, we employ this strategy for quantum roulette with N = 3.

scholarly journals Classical capacity of a qubit depolarizing channel with memory

2009 ◽  
Vol 79 (4) ◽  
Author(s):  
Jeroen Wouters ◽  
Mark Fannes ◽  
Ismail Akhalwaya ◽  
Francesco Petruccione
Keyword(s):  
Classical Capacity ◽  
With Memory ◽  
Depolarizing Channel

scholarly journals Quantum entanglement and classical communication through a depolarizing channel

2000 ◽  
Vol 47 (2-3) ◽  
pp. 325-331 ◽  
Author(s):  
Dagmar Bruss ◽  
Lara Faoro ◽  
Chiara Macchiavello ◽  
G. Massimo Palma
Keyword(s):  
Quantum Entanglement ◽  
Classical Communication ◽  
Depolarizing Channel
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