  The unique features of entanglement and non-locality in quantum systems,
where there are pairs of bipartite states perfectly distinguishable by general
entangled measurements yet indistinguishable by local operations and classical
communication, hold significant importance in quantum entanglement theory,
distributed quantum information processing, and quantum data hiding. This paper
delves into the entanglement cost for discriminating two bipartite quantum
states, employing positive operator-valued measures (POVMs) with positive
partial transpose (PPT) to achieve optimal success probability through general
entangled measurements. First, we introduce an efficiently computable quantity
called the spectral PPT-distance of a POVM to quantify the localness of a
general measurement. We show that it can be a lower bound for the entanglement
cost of optimal discrimination by PPT POVMs. Second, we establish an upper
bound on the entanglement cost of optimal discrimination by PPT POVMs for any
pair of states. Leveraging this result, we show that a pure state can be
optimally discriminated against any other state with the assistance of a single
Bell state. This study advances our understanding of the pivotal role played by
entanglement in quantum state discrimination, serving as a crucial element in
unlocking quantum data hiding against locally constrained measurements.
