Certifying the Classical Simulation Cost of a Quantum Channel

• URL: http://arxiv.org/abs/2102.12543v1
• Date: Wed, 24 Feb 2021 20:22:43 GMT
• Title: Certifying the Classical Simulation Cost of a Quantum Channel
• Authors: Brian Doolittle and Eric Chitambar
• Abstract summary: A fundamental objective in quantum information science is to determine the cost in classical resources simulating a particular quantum system. This paper provides a collection of device-independent tests that place lower and upper bounds on the signaling dimension of a channel.
• Score: 4.974890682815778
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Bell inequalities 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.

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