Extensive nonadditivity of privacy.

Quantum information theory establishes the ultimate limits on communication and cryptography in terms of channel capacities for various types of information. The private capacity is particularly important because it quantifies achievable rates of quantum key distribution. We study the power of quantum channels with limited private capacity, focusing on channels that dephase in random bases. These display extensive nonadditivity of private capacity: a channel with 2logd input qubits that has a private capacity less than 2, but when used together with a second channel with zero private capacity, the joint capacity jumps to (1/2)logd. In contrast to earlier work which found nonadditivity vanishing as a fraction of input size or conditional on unproven mathematical assumptions, this provides a natural setting manifesting nonadditivity of privacy of the strongest possible sort.

[1]  P. Shor,et al.  QUANTUM-CHANNEL CAPACITY OF VERY NOISY CHANNELS , 1997, quant-ph/9706061.

[2]  D. Vernon.  Inform , 1995, Encyclopedia of the UN Sustainable Development Goals.

[3]  Pawel Horodecki,et al.  Purely quantum superadditivity of classical capacities of quantum multiple access channels. , 2009, Physical review letters.

[4]  Joseph M Renes,et al.  Structured codes improve the Bennett-Brassard-84 quantum key rate. , 2008, Physical review letters.

[5]  Rüdiger L. Urbanke,et al.  The renaissance of Gallager's low-density parity-check codes , 2003, IEEE Commun. Mag..

[6]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[7]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[8]  Rune B. Lyngsø,et al.  Lecture Notes I , 2008 .

[9]  S. Lloyd.  Capacity of the noisy quantum channel , 1996, quant-ph/9604015.

[10]  Proceedings of the second Japan-USSR Symposium on Probability Theory , 1973 .

[11]  Ashish V. Thapliyal,et al.  Superactivation of bound entanglement. , 2000, Physical review letters.

[12]  Michal Horodecki,et al.  Low-Dimensional Bound Entanglement With One-Way Distillable Cryptographic Key , 2008, IEEE Transactions on Information Theory.

[13]  Igor Devetak,et al.  Inequalities and separations among assisted capacities of quantum channels. , 2006, Physical review letters.

[14]  M. Hastings.  Superadditivity of communication capacity using entangled inputs , 2009 .

[15]  Debbie W. Leung,et al.  Quantum data hiding , 2002, IEEE Trans. Inf. Theory.

[16]  John A Smolin,et al.  Can nonprivate channels transmit quantum information? , 2008, Physical review letters.

[17]  J. Oppenheim,et al.  Secure key from bound entanglement. , 2003, Physical Review Letters.

[18]  Igor Devetak.  The private classical capacity and quantum capacity of a quantum channel , 2005, IEEE Transactions on Information Theory.

[19]  B. Simon.  Representations of finite and compact groups , 1995 .

[20]  P. Shor,et al.  Nonadditivity of bipartite distillable entanglement follows from a conjecture on bound entangled Werner states. , 2000, Physical review letters.

[21]  Graeme Smith,et al.  Quantum Communication with Zero-Capacity Channels , 2008, Science.

[22]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[23]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .