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We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for discrete quantum measurement systems with limited classical common randomness. The main coding theorem provides the achievable rate region of a lossy measurement source coding for an exact construction of the destination distribution (or the equivalent quantum state) while maintaining a threshold of distortion from the source state according to a generally defined distortion observable. The constraint on the output space fixes the output distribution to an i.i.d. predefined probability mass function. Therefore, this problem can also be viewed as information-constrained optimal transport which finds the optimal cost of transporting the source quantum state to the destination state via an entanglement-breaking channel with limited communication rate and common randomness.more » « less
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Ghazvini, M; Dlius, R; Richards, S; Ratanpara, A; Hafez, M; Kim, M (, American Physical Society Division of Fluid Dynamics)
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Ruth, D.; Zielinski, R.; Gu, C.; Allada, M.; Badman, T.; Huang, M.; Liu, J.; Zhu, P.; Allada, K.; Zhang, J.; et al (, Nature Physics)
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