Entanglement of Subspaces and Error Correcting Codes
arXiv:0704.0251 · doi:10.1103/PhysRevA.76.042309
Abstract
We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces it is additive. Furthermore, we show that maximally entangled subspaces can play an important role in the study of quantum error correction codes. We discuss both degenerate and non-degenerate codes and show that the subspace spanned by the logical codewords of a non-degenerate code is a 2k-totally (maximally) entangled subspace. As for non-degenerate codes, we provide a mathematical definition in terms of subspaces and, as an example, we analyze Shor's nine qubits code in terms of 22 mutually orthogonal subspaces.
8 pages, Published Version
References in corpus (4)
Cited by in corpus (24)
- All Maximally Entangled Four Qubits States
- Generic local distinguishability and completely entangled subspaces
- Quantum Codes of Maximal Distance and Highly Entangled Subspaces
- -Uniform states and quantum information masking
- Reexamination of entanglement of superpositions
- Entanglement between Two Uses of a Noisy Multipartite Quantum Channel Enables Perfect Transmission of Classical Information
- Entanglement of subspaces in terms of entanglement of superpositions
- Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
- An approach to constructing genuinely entangled subspaces of maximal dimension
- Entangled subspaces and generic local state discrimination with pre-shared entanglement
- The minimum entropy output of a quantum channel is locally additive
- Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
- A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
- Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
- Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
- Quantifying subspace entanglement with geometric measures
- Recycled detection of genuine multiparty entanglement of unlimitedly stretched array of parties and arbitrarily long series of sequential observers
- Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities
- Maximally entangled real states and SLOCC invariants: the 3-qutrit case
- The minimum Renyi entropy output of a quantum channel is locally additive
- Entangled Subspaces through Algebraic Geometry
- Entanglement witnesses for stabilizer states and subspaces beyond qubits
- Absolutely maximally entangled pure states of multipartite quantum systems
- Frustration graph formalism for qudit observables