Fig. 2
From: Uncertainty equality with quantum memory and its experimental verification
a Quantum circuit of directly measuring the purity. b Molecular structure for NMR quantum register. c Experimental schematic for verifying the measurement uncertainty relation. MUB measurements are performed on subsystem A to get ρθB, and meanwhile the same process is applied on the mirror subsystem A′. Then controlled-SWAP gates are performed for the measurements of the linear entropies SL(θ|B) in LHS of Eq. (4). The purity information on the original state ρAB, i.e., the RHS of Eq. (4), are obtained without MUB measurement in the dashed lines. The purities of the bipartite system AB: \({\mathrm{Tr}}(\rho _{AB}^2)\) and \({\mathrm{Tr}}(\rho _{\theta B}^2)\), are obtained by two controlled-SWAP gates Cswap applying on subsystems AA′ and BB′ while only one Cswap is operated on subsystem BB′ (denoted by the solid line) for the purity of subsystem \({\mathrm{Tr}}(\rho _B^2)\) and \({\mathrm{Tr}}(\rho _{B|\theta }^2)\), where ρB|θ = TrA(ρθB)
