Certifying the classical simulation cost of a quantum channel

Brian Doolittle, Eric Chitambar

Research output: Contribution to journalArticlepeer-review


A fundamental objective in quantum information science is to determine the cost in classical resources of simulating a particular quantum system. The classical simulation cost is quantified by the signaling dimension which specifies the minimum amount of classical communication needed to perfectly simulate a channel's input-output correlations when unlimited shared randomness is held between encoder and decoder. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel. Among them, a single family of tests is shown to determine when a noisy classical channel can be simulated using an amount of communication strictly less than either its input or its output alphabet size. In addition, a family of eight signaling dimension witnesses is presented that completely characterize when any four-outcome measurement channel, such as a Bell measurement, can be simulated using one communication bit and shared randomness. Finally, we bound the signaling dimension for all partial replacer channels in d dimensions. The bounds are found to be tight for the special case of the erasure channel.

Original languageEnglish (US)
Article numberA71
JournalPhysical Review Research
Issue number4
StatePublished - Dec 2021

ASJC Scopus subject areas

  • General Physics and Astronomy


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