Quantum and classical message protect identification via quantum channels

• Authors: Andreas Winter
• Venue: Quantum Information & Computation
• Year: 2004

We discuss concepts of message identification in the sense of Ahlswede and Dueckvia general quantum channels, extending investigations for classical channels, initial work forclassical--quantum (cq) channels and "quantum fingerprinting". We show that the identificationcapacity of a discrete memoryless quantum channel for classical informationcan be larger than that for transmission; this is in contrast to all previously consideredmodels, where it turns out to equal the common randomness capacity (equals transmissioncapacity in our case): in particular, for a noiseless qubit, we show the identificationcapacity to be 2, while transmission and common randomness capacity are 1. Then weturn to a natural concept of identification of quantum messages (i.e. a notion of "fingerprint"for quantum states). This is much closer to quantum information transmissionthan its classical counterpart (for one thing, the code length grows only exponentially,compared to double exponentially for classical identification). Indeed, we show how theproblem exhibits a nice connection to visible quantum coding. Astonishingly, for thenoiseless qubit channel this capacity turns out to be 2: in other words, one can compress twoqubits into one and this is optimal. In general however, we conjecture quantumidentification capacity to be different from classical identification capacity.