2008/01/10 by Shanthanu Bhardwaj, V. Ravishankar
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Concurrence #Discrete mathematics #Invariant (physics) #Mathematical physics #Mathematics #Measure (data warehouse) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum entanglement #Quantum mechanics #Qubit #State (computer science) #quant-ph
paper · pdf · doi:10.1103/physreva.77.022322
12 pages, 6 figures. Enlarged version of quant-phy/0703017
arxiv created 2008/01/10 · openalex publication_date 2008/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose that the entanglement of mixed states is characterized properly in terms of a probability density function P_\ensuremathρ(E). There is a need for such a measure since the prevalent measures (such as concurrence and negativity) for two-qubit systems are rough benchmarks and not monotones of each other. Focusing on the two-qubit states, we provide an explicit construction of P_\ensuremathρ(E) and show that it is characterized by a set of parameters of which concurrence is but one particular combination. P_\ensuremathρ(E) is manifestly invariant under SU(2)\ifmmode×\else\texttimes\fiSU(2) transformations. It can, in fact, reconstruct the state up to local operations---with the specification of at most four additional parameters. Finally, the measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.