Exponent for classical-quantum multiple access channel

Multiple-user information theory, or network information theory, was started by C. E. Shannon, the founder of Information Theory [1]. The only multiple-user channel in classical information theory whose single-letter capacity region is completely known, is the multiple access channel (MAC). MAC is a channel with a single output and two (or more) inputs. Its capacity region was determined by R. Ahlswede [2] and H. Liao [3], independently. Its strong converse coding theorem was proven by G. Dueck [4]. Subsequently its exponential bounds of probability of error were studied by many different authors (e.g, [5]-[10]). The capacity region of memoryless classical quantum MAC (CQMAC) was determined by A. Winter [11] and its strong converse was proven by R. Ahlswede and N. Cai [12]. The capacity regions of quantum MAC with a classical input and a quantum input (“cqq”), and the capacity regions of quantum MAC with two quantum inputs (”qqq”) were determined in [13] and [14]. Quantum MAC with various types of resources were also studied (e.g., [15]-[17]). However according to our best knowledge the exponential bounds of probability of error for CQMAC was only considered by T. Kubo and H.Nagaoka [18]. They considered a very general (not necessary to be memoryless) model of CQMAC with three different settings at encoders, and obtained a lower bound of probability of error. Then they applied it to the quantum information spectrum setting, which can be considered as an extension of work