Timeline for Quantum Error Correction
Current License: CC BY-SA 2.5
8 events
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| Oct 13, 2010 at 4:14 | comment | added | Peter Shor | And for people reading my comment three comments above, I should say that large block length means the encoder inputs quantum states which are entangled over the input spaces of many uses of the quantum channel, and the decoder uses quantum operations on the tensor product of the output spaces of these channels to correct the error. | |
| Oct 13, 2010 at 4:08 | comment | added | Peter Shor | There's a quantum capacity formula (like the Shannon capacity) which is unfortunately not single-symbol. My conjecture is that for most simple channels whose capacity is not near 0, the quantum capacity is actually given by the single-symbol version of the formula. A good reference on quantum information theory may be John Preskill's lecture notes, especially chapter 5 (but they don't cover quantum error correcting codes or the quantum capacity of a quantum channel; just the classical capacity of a quantum channel). | |
| Oct 13, 2010 at 3:55 | comment | added | sleepless in beantown | @Peter Shor, thanks again for the clarification. Could you perhaps point me to a good review article or book to look at the details of this? Is the quantum channel capacity a function of the medium, or perhaps of the encoding scheme? (once again, apologies if this is an embarassingly naive question; I am conversant with information theory, though not as well informed about quantum computation and information processing) | |
| Oct 13, 2010 at 3:50 | comment | added | Peter Shor | Not all quantum channels have positive quantum capacity. Some channels (entanglement breaking channels) are not completely noisy, but noisy enough that if you input half of an entangled state, no entanglement comes out. These cannot transmit quantum information. Other channels are too noisy to transmit pure-state entanglement, but still can transmit some kinds of quantum entanglement. Finally, some channels have positive quantum capacity. If you transmit at a rate slower than the capacity, with large enough block length you can find codes that transmit quantum states arbitrarily well. | |
| Oct 13, 2010 at 3:23 | comment | added | sleepless in beantown | @Peter Shor, thanks for the confirmation that I'm understanding this concept clearly. | |
| Oct 13, 2010 at 3:18 | comment | added | Peter Shor | And more or less the same thing happens in quantum error correcting codes. | |
| Oct 12, 2010 at 22:01 | history | edited | sleepless in beantown | CC BY-SA 2.5 |
point about Shannon entropy, and error-coding reducing possible information density
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| Oct 12, 2010 at 21:41 | history | answered | sleepless in beantown | CC BY-SA 2.5 |