Algebraic measures of entanglement

Mathematics of Quantum Computation

Volumn , Issue , 2002, Pages 3-24

  Brylinski, Jean Luc ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

QUANTUM COMPUTERS; TENSORS;

ALGEBRAIC MEASURES; DEGREE OF ENTANGLEMENT; LINEAR COMBINATIONS; LOCAL UNITARY; NORMAL FORM; PARTIAL RESULTS; TENSOR PRODUCTS;

QUANTUM ENTANGLEMENT;

EID: 84991955466     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (18)

1. A. Acin, A. Andrianov, L. Costa, E. Jane, J.I. Latorre, R. Tarrach, Generalized Schmidt decomposition and classification of three-quantum-bit states, Phys. Rev. Lett., 85 (2000) 1560–1563.
2. A. Acin, A. Andrianov, E. Jane, R. Tarrach, Three-qubit pure-state canonical forms, J. Phys. A: Math. Gen., 34 (2001), 6725; quant-ph/0009107.
3. 2.7799)complexity for matrix multiplication, Inf. Proc. Lett., 8 (1979), 234– 235.
4. J-L. Brylinski and R. Brylinski, Polynomial invariants for qubits, In Chapter 11 of this book.
5. P. Bürgisser, M. Clausen and M. A. Shokrollahi, Algebraic Complexity Theory, Grundl. vol. 315, Springer–Verlag, New York-Heidelberg-Berlin (1997).
6. A.R. Calderbank, E. M Rains, P.W. Shor and N.J.A. Sloane, Quantum Error Correction via Codes over GF(4), IEEE Trans. Inform. Theory, 44 (1998), 1369–1387; quant-ph/9608006.
7. F. Catanese, Review of the book [C-R-S-S], Bull. Amer. Soc. (2000).
8. A. Cayley, On the theory of elimination, Collected Papers, vol.1, no. 59, Cambridge University Press, Cambridge, UK (1889), 370– 374.
9. V. Coffman, J. Kundu and W. K. Wootters, Distributed Entanglement, quant-ph/9907047.
10. I.M. Gelfand, M. Kapranov and A. Zelevinsky, Discriminants, Resultants and Multidimensional Determinants, Birkhäuser, Boston (1991).
11. D. Gottesman, An Introduction to Quantum Error Correction, talk given at AMS Short Course on Quantum Computation in Jan. 2000, quant-ph/0004072.
12. D. Meyer and N. Wallach Invariants for multiple qubits: the case of 3 qubits. In Chapter 3 of this book.
13. S. Popescu and R. Rohrlich, The Joy of Entanglement, Introduction to Quantum Computation and Information, H-K. Lo, S. Popescu and T. Spiller eds, World Scientific, Singapore (1998), 29–48.
14. A. Steane, Simple Quantum Error Correcting Codes, Phys. Rev. A, 54 (1996), 4741.
15. V. Strassen, Gaussian elimination is not optimal, Numer. Math., 13 (1969), 354–356.
16. V. Strassen, Rank and optimal computation of general tensors, Linear Alg. Appl., 52/53 (1983), 645–685.
17. A. Sudbery, On local invariants of pure three-qubit states, J. Phys. A: Math. Gen., 34 (2001), 643–652.
18. F. Verstraete, J. Dehaene, B. De Moor, H. Verscheld, Four qubits can be entangled in nine different ways, quant-ph/0109033.