[Paper Review] Information-theoretic aspects of the generalized amplitude damping channel

Sumeet Khatri, Kunal Sharma+1 more|arXiv (Cornell University)|Mar 18, 2019

Quantum Computing Algorithms and Architecture137 references66 citations

TL;DR

This paper provides a comprehensive information-theoretic analysis of the generalized amplitude damping channel (GADC), a key noise model in superconducting quantum computing. By leveraging data-processing inequalities, uniform continuity of information measures, and squashed entanglement, the authors derive tighter upper bounds on the GADC's classical, quantum, and private capacities—significantly reducing the gap between known lower and upper bounds, especially for quantum capacity.

ABSTRACT

The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.

Motivation & Objective

• To characterize the GADC as an entanglement-breaking or anti-degradable channel across its parameter range.
• To establish improved upper bounds on the classical, quantum, and private capacities of the GADC.
• To reduce the gap between known lower and upper bounds on the quantum capacity of the GADC.
• To develop new upper bounds on two-way assisted quantum and private capacities using squashed entanglement.
• To compare multiple bounding techniques (e.g., max-Rains, mutual information, approximate covariance) for their effectiveness on the GADC.

Proposed method

• Derive analytical expressions for Cβ and Cζ, two upper bounds on classical capacity based on no-signaling and PPT-preserving codes.
• Prove that Cζ = Cβ for the GADC, simplifying the analysis of classical capacity bounds.
• Employ ε-entanglement-breaking and ε-covariance techniques to derive additional classical capacity upper bounds.
• Use data-processing inequalities and uniform continuity of information-theoretic quantities to bound quantum and private capacities.
• Construct specific squashing channels to derive upper bounds on two-way assisted quantum and private capacities using squashed entanglement.
• Compare the performance of multiple bounding techniques, including max-Rains information, mutual information, and approximate covariance bounds.

Experimental results

Research questions

• RQ1 For which parameter ranges is the GADC entanglement breaking or anti-degradable?
• RQ2 How do different information-theoretic techniques compare in bounding the classical, quantum, and private capacities of the GADC?
• RQ3 Can tighter upper bounds on the quantum capacity of the GADC be derived than previously known?
• RQ4 What is the performance of squashed entanglement-based bounds on two-way assisted capacities of the GADC?
• RQ5 How do the max-Rains information, mutual information, and approximate covariance bounds compare in their tightness for the GADC?

Key findings

• The GADC is entanglement breaking for a specific range of its parameters, and anti-degradable for another, enabling exact capacity characterization in these regimes.
• The authors derive a new upper bound on the quantum capacity of the GADC that is tighter than the previously known bound by Rosati et al. (2018) across the entire parameter range.
• The upper bound on the two-way assisted quantum capacity is derived using squashed entanglement and is shown to be effective, particularly when compared to the max-Rains information and mutual information bounds.
• The mutual information of the GADC, previously computed in [38], provides an upper bound on the unassisted classical capacity, which is compared with other bounds.
• The study demonstrates that a wide variety of techniques—data-processing inequalities, continuity bounds, squashed entanglement, and covariance-based bounds—are all useful in bounding different capacities of the GADC.
• The results significantly reduce the uncertainty in the quantum capacity of the GADC, narrowing the gap between known lower and upper bounds.