Proposed working groups.
=========================================================================
Nathaniel Johnston
1. The NPT Bound Entanglement Problem
2. References:
Pankowski et al., A few steps more towards NPT bound entanglement, IEEE Trans. Inf. Theory 56, 4085-4100
(2010). arXiv:0711.2613 [quant-ph]
DiVincenzo et al., Evidence for bound entangled states with negative partial transpose, Phys. Rev. A 61,
062312 (2000). arXiv:quant-ph/9910026
See also arXiv:0909.3907 [quant-ph] and arXiv:1006.0898 [quant-ph]
3. Zyczkowski will be interested. Hou, Qi, Li, Poon, and Sze may also be interested. Anyone else who wishes
to
contribute would be very welcome.
4. I can lead the discussion on July 17, 18, or 19 (I arrive on July 16 and leave on July 20).
==========================================================================
Chi-Kwong Li
1. Preserver problems arising in QIS
2. References:
Friedland et al., The Automorphism Group of Separable States in Quantum
Information Theory, Journal of Mathematical Physics 52, 042203 (2011).
Li, Poon, Sze, Linear preservers of Tensor product of Unitary Orbits, and
Product Numerical Range, Linear Algebra Appl, to appear. available at
http://people.wm.edu/~cklixx/ucud.pdf.
3. Poon and Sze may help lead the discussion. Johnston and Hou may
also be interested.
4. I can lead the discussion on any day except July 21,22
(sightseeing) and 20 (need to go to Guizhou).
======================================================================================
Chi-Kwong Li, Yiu-Tung Poon, Edward Poon, and Nung-Sing Sze
1. Quantum operations and completely positive linear map.
2. Refereces
[1] P. Alberti and A. Uhlmann, A problem relating to positive linear maps on matrix algebras,
Rep. Math. Phys. 18 (1980), 163.
[2] A. Chefles, R. Jozsa, and A. Winter, On the existence of physical transformations between
sets of quantum states, International J. Quantum Information 2 (2004), 11-21.
[3] Zejun Huang, Chi-Kwong Li, Edward Poon, Nung-Sing Sze,
Physical transformations between quantum states,
http://arxiv.org/abs/1203.5547
[4] C.K. Li and Y.T. Poon, Interpolation by completely positive maps, Linear
and Multilinear Algebra 59 (2011), 1159-1170.
===================================================================================
Mikio Nakahara, Yidun Wan, and Utkan Gungordu, Kinki University.
1. Mathematical Fun with NMR
Subjects include, NMR Hamiltonian as Lie algebra generator,
Application of Cartan decomposition to SU(4) gate implementaiton,
Power of DQC1: Evaluation of Jones polynomials using NMR.
2. References
(a) Chapter 12 of Quantum Computing: From Linear Algebra to Physical Realizations by
M. Nakahara and T. Ohmi
(b) E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)
(c) G. Passante et al., Phys. Rev. Lett. 103, 250501 (2009)
(d) Raimund Marx et al., Phys. Rev. A 81, 032319 (2010)
====================================================================================
Yiu-Tung Poon
1. Separability problems in terms of positive maps and realignment criteria.
2. References
Li, Poon and Sze, A note on the realignment criterion, J. Phys. A: Math. Theor. 44
315304 (2011).
3. Chi-Kwong Li and Nung-Sing Sze may help lead the discussion.
Jinchuan Hou, Xiaofei Hou, Kan He will be interested.
4. Any time from July 17-27.
=========================================================================
Nung-Sing Sze
1. Quantum Error Correction
2. References
Li, Nakahara, Poon, Sze, Tomita,
Efficient Quantum Error Correction for Fully Correlated Noise,
Phys. Lett. A, 375:3255-3258 (2011).
Li, Nakahara, Poon, Sze, Tomita,
Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace,
Physical Review A 84, 044301 (2011).
Li, Nakahara, Poon, Sze, Tomita,
Recovery in quantum error correction for general noise without measurement,
Quantum Information & Computation 12 (2012), 149-158.
3. Li, Nakahara, Poon, Johnston will be interested.
4. Any time from July 17-27.
====================================================================================
Shengjun Wu
1. Entanglement versus quantum correlations
2. References
S. Wu, U.V. Poulsen, and K. Moelmer, Phys. Rev. A 80, 032319 (2009).
S. Wu, arXiv 1110.6873[quant-ph].
K. Modi, et al., arXiv 1112.6238[quant-ph] (for a nice review).
3. Yu Guo may help lead the discussions, and I hope more people join in and help lead the discussions.
4. The discussion will be on July 26 or July 27.
==================================================================
Karol Zyczkowski, Uniwersytet Jagielloński
1. On the measures of quantum entanglement
2. References:
[1] F. Mintert, ARR Carvalho, M Kus and A. Buchleitner,
Measures and dynamics of entangled states
Phys. Rep. 415, 207 (2005).
[2] M. B. Plenio, S. Virmani, An introduction to entanglement measures
Quant. Inf. Comp. 7, 1 (2007).
[3] R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki,
Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
[4] O. Guehne and G. Toth, Phys. Rep. 474, 1 (2009).
[5] R. Augusiak and M. Lewenstein,
Towards measurable bounds on entanglement measures
Quantum Inf. Process. 8, 493 (2009).
[6] Rudnicki, P. Horodecki and K. Zyczkowski,
Collective Uncertainty Entanglement Test,
Phys. Rev. Lett. 107, 150502 (2011)
3. He, Hou, Johnston, Li, Poon, Sze, Wu will be interested.
4. The discussion will be on July 17.
=====================================================