We present an universal protocol, capable of compressing $N$ copies of a completely unknown mixed state into $O(\log N)$ qubits in a lossless fashion. Our result demonstrates that the exponential compression of identically prepared pure states, recently implemented in a prototype experiment by Rozema et. al. [Phys. Rev. Lett. 113, 160504 (2014)], can be extended to arbitrary mixed states, despite the fact that the latter cover an exponentially large space. Furthermore, we highlight a striking difference between the pure and the mixed state case, showing that, if the spectrum is known with sufficient precision, the number of qubits needed for compression of a mixed state will drop down discontinuously as soon as a small recovery error is allowed.
CITATION STYLE
Yang, Y., Ebler, D., & Chiribella, G. (n.d.). Optimal Compression for Ensembles of Identically Prepared Mixed States, (1), 1–17.
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