Memory effects in spin-chain channels for information transmission

We investigate the multiple use of a ferromagnetic spin chain for quantum and classical communications without resetting. We find that the memory of the state transmitted during the first use makes the spin chain a qualitatively different quantum channel during the second transmission, for which we find the relevant Kraus operators. We propose a parameter to quantify the amount of memory in the channel and find that it influences the quality of the channel, as reflected through fidelity and entanglement transmissible during the second use. For certain evolution times, the memory allows the channel to exceed the memoryless classical capacity (achieved by separable inputs) and in some cases it can also enhance the quantum capacity.

Figure 1

(Color online) Communication setup includes the sender and receiver registers in both sides of the spin chain. (a) Setup for state transfer and the classical capacity problem. (b) Setup for entanglement distribution and the quantum capacity problem.

Figure 2

(Color online) As a function of evolution time $\tau$: (a) Average fidelity in the second use for memoryless channel in comparison with the memory case when the state $\mid 1⟩$ is transferred and also with average pure input states in the first use. (b) The average fidelity for the second use and the parameter $1-\Delta ∕4$ after transferring the state $\mid 1⟩$. (c) The entanglement distribution for both the memory and memoryless channel.

Figure 3

(Color online) Maximum of the average fidelity in the second use when $\mid 1⟩$ is sent in the first use versus memory parameter $\Delta$.

Figure 4

(Color online) (a) Holevo bound in memory spin chains in compare with classical capacity for separable input states. (b) Coherent information for a special input states in memory channel in compare with quantum capacity for memoryless one.