Entanglement cost of realizing quantum processes (2311.10649v2)

Abstract: Quantum entanglement, a peculiar connection between particles, underpins powerful technologies such as quantum computing and secure communication. However, quantifying the minimum entanglement required to prepare quantum states and implement quantum processes remains a significant challenge. We develop an efficiently computable tool that reliably estimates the amount of entanglement needed for realizing arbitrary quantum processes respecting certain physical principles. Our tool applies to the entanglement required to prepare a broad range of quantum states in the asymptotic regime, surpassing previous methods' limitations. We also confirm that entanglement, once consumed to realize the considered class of quantum operations, cannot be fully recovered, even asymptotically. This irreversible behavior is evident for full-rank entangled states and practically relevant amplitude damping channels, even under quantum operations that completely preserve the positivity of partial transpose. We showcase our approach's power through examples such as estimating entanglement requirements for realizing bipartite dephasing SWAP channels and solving Hamiltonian simulations under thermal interaction, highlighting its advantages over existing techniques. Our work provides a practical toolkit for benchmarking entanglement requirements for generic states and quantum dynamics, paving the way for assessing and optimizing the performances of quantum technologies.