Quantum computation and quantum information
Quantum computation and quantum information
Theory of Information and Coding
Theory of Information and Coding
Upper and lower bounds on quantum codes
Upper and lower bounds on quantum codes
Basic Algebra
IEEE Transactions on Information Theory
Modern Coding Theory
Quantum error correction via codes over GF(4)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Upper bounds on the size of quantum codes
IEEE Transactions on Information Theory
Monotonicity of the quantum linear programming bound
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
The private classical capacity and quantum capacity of a quantum channel
IEEE Transactions on Information Theory
A Resource Framework for Quantum Shannon Theory
IEEE Transactions on Information Theory
High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement
IEEE Transactions on Information Theory
Hi-index | 0.00 |
The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code's information qubits with its ebits. To introduce this notion, we show how entanglement-assisted repetition codes and accumulator codes are dual to each other, much like their classical counterparts, and we give an explicit, general quantum shift-register circuit that encodes both classes of codes. We later show that our constructions are optimal, and this result completes our understanding of these dual classes of codes. We also establish the Gilbert---Varshamov bound and the Plotkin bound for EAQEC codes, and we use these to examine the existence of some EAQEC codes. Finally, we provide upper bounds on the block error probability when transmitting maximal-entanglement EAQEC codes over the depolarizing channel, and we derive variations of the hashing bound for EAQEC codes, which is a lower bound on the maximum rate at which reliable communication over Pauli channels is possible with the use of pre-shared entanglement.