Optimal Entanglement Formulas for Entanglement-Assisted Quantum Coding
arXiv:0804.1404 · doi:10.1103/PhysRevA.77.064302
Abstract
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block code. Corollaries of this theorem give formulas that apply to a code imported from two classical binary block codes, to a code imported from a classical quaternary block code, and to a continuous-variable entanglement-assisted quantum block code. Finally, we conjecture two formulas that apply to entanglement-assisted quantum convolutional codes.
4 pages, Changed "Formulae to Formulas" in title, published in Physical Review A
References in corpus (3)
Cited by in corpus (47)
- Entanglement-assisted quantum error-correcting codes over arbitrary finite fields
- Entanglement-assisted quantum turbo codes
- Euclidean and Hermitian Hulls of MDS Codes and Their Applications to EAQECCs
- Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
- Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes
- Duality in Entanglement-Assisted Quantum Error Correction
- High performance entanglement-assisted quantum LDPC codes need little entanglement
- Entanglement-assisted quantum low-density parity-check codes
- Entropic proofs of Singleton bounds for quantum error-correcting codes
- New entanglement-assisted MDS quantum codes from constacyclic codes
- On the logical operators of quantum codes
- Encoding One Logical Qubit Into Six Physical Qubits
- Dualities and Identities for Entanglement-Assisted Quantum Codes
- Asymmetric entanglement-assisted quantum error-correcting codes and BCH codes
- Quantum Shift Register Circuits
- Quantum Coding with Entanglement
- A characterization of entanglement-assisted quantum low-density parity-check codes
- Nonlocal quantum information in bipartite quantum error correction
- Two families of Entanglement-assisted quantum MDS codes from constacyclic codes
- Quantum error correction via less noisy qubits
- Entanglement-assisted concatenated quantum codes
- High-rate quantum low-density parity-check codes assisted by reliable qubits
- Minimal-memory, non-catastrophic, polynomial-depth quantum convolutional encoders
- Quantum Convolutional Coding with Shared Entanglement: General Structure
- Optimized Entanglement-Assisted Quantum Error Correction
- Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance
- The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
- Entanglement-assisted quantum codes from Galois LCD codes
- Degenerate Local-dimension-invariant Stabilizer Codes and an Alternative Bound for the Distance Preservation Condition
- Protecting Quantum Information with Entanglement and Noisy Optical Modes
- Entanglement-assisted quantum error-correcting codes from units
- Two families of Entanglement-assisted Quantum MDS Codes from cyclic Codes
- Examples of minimal-memory, non-catastrophic quantum convolutional encoders
- Galois hulls of MDS codes and their quantum error correction
- Entanglement-assisted Quantum Codes from Algebraic Geometry Codes
- Transforming Collections of Pauli Operators into Equivalent Collections of Pauli Operators over Minimal Registers
- A new method for constructing EAQEC MDS codes
- Quantum Error-Control Codes
- Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1
- Explicit constructions of optimal linear codes with Hermitian hulls and their application to quantum codes
- Multivariate Goppa codes
- Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes
- Changing the Local-Dimension of an Entanglement-Assisted Stabilizer Code Removes Entanglement Need
- Steane enlargement of Entanglement-Assisted Quantum Error-Correcting Codes
- Bounds on concatenated entanglement-assisted quantum error-correcting codes
- On Euclidean Hulls of MDS Codes
- New Galois Hulls of GRS Codes and Application to EAQECCs