Entanglement cost and quantum channel simulation
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This paper proposes a revised definition for the entanglement cost of a quantum channel N. In particular, it is defined here to be the smallest rate at which entanglement is required, in addition to free classical communication, in order to simulate n calls to N, such that the most general discriminator cannot distinguish the n calls to N from the simulation. The most general discriminator is one who tests the channels in a sequential manner, one after the other, and this discriminator is known as a quantum tester [Chiribella et al., Phys. Rev. Lett., 101, 060401 (2008)] or one who is implementing a quantum strategy [Gutoski et al., Symp. Th. Comp., 565 (2007)]. As such, the proposed revised definition of entanglement cost of a quantum channel leads to a rate that cannot be smaller than the previous notion of a channel's entanglement cost [Berta et al., IEEE Trans. Inf. Theory, 59, 6779 (2013)], in which the discriminator was limited to distinguishing parallel uses of the channel from the simulation. Under this revised notion, I prove that the entanglement cost of certain teleportation-simulable channels is equal to the entanglement cost of their underlying resource states. Then I find single-letter formulas for the entanglement cost of some fundamental channel models, including dephasing, erasure, and three-dimensional Werner-Holevo channels, as well as single-mode pure-loss and pure-amplifier bosonic Gaussian channels. Finally, I discuss how to generalize the basic notions to arbitrary resource theories.
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