Approximate private quantum channels on fermionic Gaussian systems
- URL: http://arxiv.org/abs/2003.11907v1
- Date: Thu, 26 Mar 2020 13:59:54 GMT
- Title: Approximate private quantum channels on fermionic Gaussian systems
- Authors: Kabgyun Jeong
- Abstract summary: We introduce a notion of approximate private quantum channel ($varepsilon$-FPQC) on fermionic Gaussian systems.
We construct its explicit form of the fermionic (Gaussian) private quantum channel.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 introduce a notion of
approximate private quantum channel ($\varepsilon$-PQC) on fermionic Gaussian
systems (i.e., $\varepsilon$-FPQC), and construct its explicit form of the
fermionic (Gaussian) private quantum channel. First of all, we suggest a
general structure for $\varepsilon$-FPQC on the fermionic Gaussian systems with
respect to the Schatten $p$-norm class, and then we give an explicit proof of
the statement in the trace norm. In addition, we study that the cardinality of
a set of fermionic unitary operators agrees on the $\varepsilon$-FPQC condition
in the trace norm case.
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