Average fidelity estimation of twirled noisy quantum channel using unitary 2<i>t</i>-design<xref rid="cpb_28_1_010304fn1" ref-type="fn">*</xref> <fn id="cpb_28_1_010304fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).</p> </fn>

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).

Zhang Linxi^{1, 2, †}, Zhu Changhua¹, Pei Changxing¹

A t-tensor product CPTP noise channel model using unitary 2t-design is composed of three linear mappings Λ^⊗t, U^⊗t, and (U^†)^⊗t. For any d^tn-dimensional input density operator ρ^⊗t, the representation of the unitary operation U ^ ⊗ t = U ⊗ t ⊗ ( U † ) ⊗ t and the noise channel Λ ^ ⊗ t = ∑ j , k = 1 d n A k ⊗ t ⊗ ( A j ⊗ t ) ∗ = ( ∑ k = 1 d n ⊗ i = 1 t A k , i ) ⊗ ( ∑ j = 1 d n ⊗ m = 1 t A j , m ) ∗ are d^2tn × d^2tn matrices, where ⊗ i = 1 t A k , i = A k , 1 ⊗ A k , 2 ⊗ ⋯ ⊗ A k , t .