Approximate Private Quantum Channels on Fermionic Gaussian Systems

• 作者: Kabgyun Jeong
• 来源期刊: 量子信息科学期刊(英文)
• 学科: 物理学
• 关键词: Fermionic Private Quantum Channel Approximate FPQC Isotropic Measure ε-Net Analysis McDiarmid’s Inequality
• 年，卷（期）: 2021,（1）
• 页码范围: 1-12
• 页数: 12页
• 分类号: O41

摘要

The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (<em>ε</em>-PQC) on <em>fermionic</em> Gaussian systems (<em>i.e.</em>, <em>ε</em>-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for <em>ε</em>-FPQC on the fermionic Gaussian systems with respect to the Schatten <em>p</em>-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the <em>ε</em>-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.