Simplification of Additivity Conjecture in Quantum Information Theory

We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. In this paper, by using some unital extension of quantum channels, we show that proving one of these conjectures for all unital quantum channels would imply that it is also true for all quantum channels.

[1]  P. Shor.  Additivity of the classical capacity of entanglement-breaking quantum channels , 2002, quant-ph/0201149.

[2]  M. Fukuda.  Extending additivity from symmetric to asymmetric channels , 2005, quant-ph/0505022.

[3]  K. Audenaert,et al.  Communications in Mathematical Physics On Strong Superadditivity of the Entanglement of Formation , 2004 .

[4]  A. Holevo.  Remarks on the classical capacity of quantum channel , 2002, quant-ph/0212025.

[5]  C. King.  The capacity of the quantum depolarizing channel , 2003, IEEE Trans. Inf. Theory.

[6]  Grigori G. Amosov.  Remark on the additivity conjecture for a quantum depolarizing channel , 2006, Probl. Inf. Transm..

[7]  M. Fannes,et al.  Additivity of minimal entropy output for a class of covariant channels , 2004, quant-ph/0410195.

[8]  A. Fujiwara,et al.  Additivity of the capacity of depolarizing channels , 2002 .

[9]  A. Winter,et al.  Remarks on Additivity of the Holevo Channel Capacity and of the Entanglement of Formation , 2002, quant-ph/0206148.

[10]  Keiji Matsumoto,et al.  Entanglement cost of antisymmetric states and additivity of capacity of some quantum channels , 2003, quant-ph/0306009.

[11]  Christopher King,et al.  Minimal entropy of states emerging from noisy quantum channels , 2001, IEEE Trans. Inf. Theory.

[12]  Nilanjana Datta,et al.  A quantum channel with additive minimum output entropy , 2004 .

[13]  M. Ruskai,et al.  Maximal output purity and capacity for asymmetric unital qudit channels , 2005, quant-ph/0505048.

[14]  J. Eisert,et al.  Classical information capacity of a class of quantum channels , 2004, quant-ph/0412133.

[15]  Nilanjana Datta,et al.  ADDITIVITY FOR TRANSPOSE DEPOLARIZING CHANNELS , 2004 .

[16]  Andrei Pomeransky.  Strong superadditivity of the entanglement of formation follows from its additivity , 2003 .

[17]  K. Audenaert,et al.  Ju n 20 03 On Strong Subadditivity of the Entanglement of Formation , 2008 .

[18]  C. King.  Additivity for unital qubit channels , 2001, quant-ph/0103156.

[19]  Mark Fannes,et al.  Se p 20 04 Note on multiple additivity of minimal Renyi entropy output of the Werner – Holevo channels , 2004 .

[20]  P. Shor.  Equivalence of Additivity Questions in Quantum Information Theory , 2004 .

[21]  R. Werner,et al.  Counterexample to an additivity conjecture for output purity of quantum channels , 2002, quant-ph/0203003.

[22]  C. King.  An application of a matrix inequality in quantum information theory , 2004 .

[23]  Christopher King.  Maximal p-norms of entanglement breaking channels , 2003, Quantum Inf. Comput..