2017/01/31 by Yuxiang Yang, Ge Bai, Giulio Chiribella +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Asymptotically optimal algorithm #Data compression #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Quantum information #Quantum network #Quantum optics and atomic interactions #Quantum state #State (computer science) #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.1109/tit.2017.2788407
published as IEEE Transactions on Information Theory, 64(7), 4766(2018) · 14 Pages, 4 Figures + Appendix
openalex created_date 2017/02/10 · openalex publication_date 2018/01/10 · arxiv created 2019/01/26 · arxiv updated 2019/04/03 · openalex updated_date 2026/08/05
We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol that requires a hybrid memory of size (f/2)log n, including both quantum and classical bits. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of compressing displaced thermal states of n identically prepared modes. In both cases, we show that (f/2)log n is the minimum amount of memory needed to achieve asymptotic faithfulness. In addition, we analyze how much of the memory needs to be quantum. We find that the ratio between quantum and classical bits can be made arbitrarily small, but cannot reach zero: unless all the quantum states in the family commute, no protocol using only classical bits can be faithful, even if it uses an arbitrarily large number of classical bits.