Detecting and estimating coherence based on coherence witnesses

Common Coherence Witnesses and Common Coherent States

“…where δ is the closest incoherent state to ρ, N = ρ − δ and A ≡ Tr(A †A). Recently, a general way of constructing a coherence witness for an arbitrary state has been provided [33,34]:…”

“…is an optimal coherence witness to detect the coherence of ρ, where ∆(ρ) = ∑ d−1 i=0 i|ρ|i |i i| is the dephasing operation in the reference basis {|i } d−1 i=0 . More general constructions of coherence witnesses are also given in [33,34].…”

“…From the general construction of optimal coherence witnesses for an arbitrary coherent state [33,34] and Corollary 3, there also exists a general way of constructing a common optimal coherence witness for different coherent states. Corollary 4.…”

“…Coherence witnesses can also be constructed from geometrical methods, where is the closest incoherent state to , and . Recently, a general way of constructing a coherence witness for an arbitrary state has been provided [ 33 , 34 ]: is an optimal coherence witness to detect the coherence of , where is the dephasing operation in the reference basis . More general constructions of coherence witnesses are also given in [ 33 , 34 ].…”

“…The coherence witness, inspired by entanglement witnesses, is arguably a powerful tool for coherence detection in experiments [ 26 , 27 , 28 , 29 , 30 , 31 , 32 ] and coherence quantification in theory [ 33 , 34 ]. It directly detects any coherent states and gives rise to measures of quantum coherence without state tomography.…”