Entanlement-Assisted Classical Capacity of Quantum Channels with Correlated Noise.pdfVIP

a r X i v : q u a n t - p h / 0 6 0 5 1 0 8 v 2 1 3 M a y 2 0 0 6 Entanglement-Assisted Classical Capacity of Quantum Channels with Correlated Noise Nigum Arshed?and A. H. Toor? Department of Physics, Quaid-i-Azam University Islamabad 45320, Pakistan. February 9, 2008 Abstract We calculate the entanglement-assisted classical capacity of symmetric and asymmetric Pauli channels where two consecutive uses of the channels are correlated. It is evident from our study that in the presence of memory, a higher amount of classical information is transmitted over quantum channels if there exists prior entanglement as compared to product and entangled state coding. Unlike classical channels, more than one distinct capacities are associated with quantum channels [1], depending on the type of information (classical or quantum) transmitted and the additional resources brought into play. Cal- culating the capacities of quantum channels is an important task of quantum information theory. Most of the work, so far, has focused on memoryless quan- tum channels [1], [2]. A channel is memoryless if noise acts independently over each use of the channel. In practice, the noise in consecutive uses of the channel is not independent and exhibits some correlation. The correlation strength is determined by the degree of memory of the channel. Quantum channels with memory were considered recently by Macchiavello and Palma [3]. They studied the depolarizing channel with Markov correlated noise and showed that beyond a certain threshold in the degree of memory of the channel, coding with maximally entangled states has edge over product states. Later this work was extended to the case of a non-Pauli channel and similar behavior was reported [4]. An upper bound for the maximum mutual informa- tion of quantum channels with partial memory was given by Macchiavello et al. [5]. This bound is achieved for minimum entropy states which turned out to be entangled above the memory threshold and proved