TY - GEN

T1 - Distributed Compression of Correlated Classical-Quantum Sources

AU - Khanian, Zahra Baghali

AU - Winter, Andreas

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/7

Y1 - 2019/7

N2 - We resume the investigation of the problem of independent local compression of correlated quantum sources, the classical case of which is covered by the celebrated Slepian-Wolf theorem. We focus specifically on classical-quantum (cq) sources, for which one edge of the rate region, corresponding to the compression of the classical part, using the quantum part as side information at the decoder, was previously determined by Devetak and Winter [Phys. Rev. A 68, 042301 (2003)]. Whereas the Devetak-Winter protocol attains a rate-sum equal to the von Neumann entropy of the joint source, here we show that the full rate region is much more complex, due to the partially quantum nature of the source. In particular, in the opposite case of compressing the quantum part of the source, using the classical part as side information at the decoder, typically the rate sum is strictly larger than the von Neumann entropy of the total source.We determine the full rate region in the generic case, showing that, apart from the Devetak-Winter point, all other points in the achievable region have a rate sum strictly larger than the joint entropy. We can interpret the difference as the price paid for the quantum encoder being ignorant of the classical side information. In the general case, we give an achievable rate region, via protocols that are built on the decoupling principle, and the principles of quantum state merging and quantum state redistribution. Our achievable region is matched almost by a single-letter converse, which however still involves asymptotic errors and an unbounded auxiliary system.

AB - We resume the investigation of the problem of independent local compression of correlated quantum sources, the classical case of which is covered by the celebrated Slepian-Wolf theorem. We focus specifically on classical-quantum (cq) sources, for which one edge of the rate region, corresponding to the compression of the classical part, using the quantum part as side information at the decoder, was previously determined by Devetak and Winter [Phys. Rev. A 68, 042301 (2003)]. Whereas the Devetak-Winter protocol attains a rate-sum equal to the von Neumann entropy of the joint source, here we show that the full rate region is much more complex, due to the partially quantum nature of the source. In particular, in the opposite case of compressing the quantum part of the source, using the classical part as side information at the decoder, typically the rate sum is strictly larger than the von Neumann entropy of the total source.We determine the full rate region in the generic case, showing that, apart from the Devetak-Winter point, all other points in the achievable region have a rate sum strictly larger than the joint entropy. We can interpret the difference as the price paid for the quantum encoder being ignorant of the classical side information. In the general case, we give an achievable rate region, via protocols that are built on the decoupling principle, and the principles of quantum state merging and quantum state redistribution. Our achievable region is matched almost by a single-letter converse, which however still involves asymptotic errors and an unbounded auxiliary system.

UR - http://www.scopus.com/inward/record.url?scp=85073162882&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2019.8849794

DO - 10.1109/ISIT.2019.8849794

M3 - Conference contribution

AN - SCOPUS:85073162882

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1152

EP - 1156

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019

Y2 - 7 July 2019 through 12 July 2019

ER -