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Second order asymptotics of mixed quantum source coding via universal codes

The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from either one of two memoryless quantum sources with given a priori probabilities. For such a source, we derive the second order asymptotic rates for fixedlength (visible) source coding. This provides the first example of second order asymptotics for a quantum information-processing task employing a resource with memory. For the case of a classical mixed source (using a finite alphabet), our results reduce to those obtained by Nomura and Han [16]. To prove the achievability part of our main result, we introduce universal quantum source codes achieving second order asymptotic rates. These are obtained by an extension of Hayashi’s construction [11] of their classical counterparts.