scholarly journals Codes for the quantum erasure channel

1997 ◽  
Vol 56 (1) ◽  
pp. 33-38 ◽  
Author(s):  
M. Grassl ◽  
Th. Beth ◽  
T. Pellizzari
Keyword(s):  
Erasure Channel ◽  
Quantum Erasure

scholarly journals Polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel

2019 ◽  
Vol 65 (11) ◽  
pp. 7584-7595
Author(s):  
Seth Lloyd ◽  
Peter Shor ◽  
Kevin Thompson
Keyword(s):  
Erasure Channel ◽  
Quantum Erasure

scholarly journals Upper bounds on the rate of low density stabilizer codes for the quantum erasure channel

2013 ◽  
Vol 13 (9&10) ◽  
pp. 793-826
Author(s):  
Nicolas Delfosse ◽  
Gilles Zemor
Keyword(s):  
Upper Bound ◽  
Percolation Theory ◽  
Hyperbolic Plane ◽  
Upper Bounds ◽  
Low Density ◽  
Critical Probability ◽  
Stabilizer Codes ◽  
Erasure Channel ◽  
Finite Quotients ◽  
Quantum Erasure

Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, $R \leq 1-2p$, for stabilizer codes: we also derive an improved upper bound of the form $R \leq 1-2p-D(p)$ with a function $D(p)$ that stays positive for $0<p<1/2$ and for any family of stabilizer codes whose generators have weights bounded from above by a constant -- low density stabilizer codes. We obtain an application to percolation theory for a family of self-dual tilings of the hyperbolic plane. We associate a family of low density stabilizer codes with appropriate finite quotients of these tilings. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. The application of our upper bound on achievable rates of low density stabilizer codes gives rise to an upper bound on the critical probability for these tilings.

scholarly journals Multilevel polarization for quantum Channels

2021 ◽  
Vol 21 (7&8) ◽  
pp. 577-606
Author(s):  
Ashutosh Goswami ◽  
Mehdi Mhalla ◽  
Valentin Savin
Keyword(s):  
Upper Bound ◽  
Noisy Channels ◽  
Code Construction ◽  
Epr Pairs ◽  
Polar Code ◽  
Alternative Construction ◽  
The Family ◽  
Quantum Version ◽  
Erasure Channel ◽  
Quantum Erasure

Recently, a purely quantum version of polar codes has been proposed in~\cite{DGMS19} based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as a channel combining operation. Here, we consider the quantum polar code construction using the same channel combining and splitting procedure as in~\cite{DGMS19}, but with a fixed two-qubit Clifford unitary. For the family of Pauli channels, we show that polarization happens in multi-levels, where synthesized quantum virtual channels tend to become completely noisy, half-noisy, or noiseless. Further, we present a quantum polar code exploiting the multilevel nature of polarization, and provide an efficient decoding for this code. We show that half-noisy channels can be frozen by fixing their inputs in either the amplitude or the phase basis, which allows reducing the number of preshared EPR pairs compared to the construction in~\cite{DGMS19}. We provide an upper bound on the number of preshared EPR pairs, which is an equality in the case of the quantum erasure channel. To improve the speed of polarization, we propose an alternative construction, which again polarizes in multi-levels, and the previous upper bound on the number of preshared EPR pairs also holds. For a quantum erasure channel, we confirm by numerical analysis that the multilevel polarization happens relatively faster for the alternative construction.

scholarly journals How to Erase Quantum Monogamy?

2021 ◽  
Vol 3 (1) ◽  
pp. 53-67
Author(s):  
Ghenadie Mardari
Keyword(s):  
Quantum System ◽  
Quantum Entanglement ◽  
The Other ◽  
Arrow Of Time ◽  
Quantum Level ◽  
Delayed Choice ◽  
Other Hand ◽  
The One ◽  
Quantum Erasure ◽  
Non Locality

The phenomenon of quantum erasure exposed a remarkable ambiguity in the interpretation of quantum entanglement. On the one hand, the data is compatible with the possibility of arrow-of-time violations. On the other hand, it is also possible that temporal non-locality is an artifact of post-selection. Twenty years later, this problem can be solved with a quantum monogamy experiment, in which four entangled quanta are measured in a delayed-choice arrangement. If Bell violations can be recovered from a “monogamous” quantum system, then the arrow of time is obeyed at the quantum level.

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