State transfer with quantum side information

Yonghae Lee, Ryuji Takagi, Hayata Yamasaki +2 more

We consider a quantum communication task between two users Alice and Bob, in which Alice and Bob exchange their respective quantum information by means of local operations and classical communication assisted by shared entanglement. Here, we assume that Alice and Bob may have quantum side information, not transferred, and classical communication is free. In this work, we derive general upper and lower bounds for the least amount of entanglement which is necessary to perfectly perform this task, called the state exchange with quantum side information. Moreover, we show that the optimal entanglement cost can be negative when Alice and Bob make use of their quantum side information. We finally provide conditions on the initial state for the state exchange with quantum side information which give the exact optimal entanglement cost.

Timothy C. Ralph, Thomas Symul, Ping Koy Lam +3 more

M. Bertolotti, Fabio Antonio Bovino, Concita Sibilia

Zhicheng Luo, Igor Devetak

We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classical-quantum Slepian-Wolf problem. The optimal noiseless communication rate is found to be reduced from the mutual information between the channel input and output by the Holevo information between the channel output and the quantum side information. Our main theorem has two important corollaries. The first is a quantum generalization of the Wyner-Ziv problem: rate-distortion theory with quantum side information. The second is an alternative proof of the tradeoff between classical communication and common randomness distilled from a quantum state. The fully quantum generalization of the problem considered isquantumstateredistribution. Here the sender and receiver share a mixed quantum state and the sender wants to transfer part of her state to the receiver using entanglement and quantum communication. We present outer and inner bounds on the achievable rate pairs.

Carlo D. Franco, Mauro Paternostro, M. S. Kim

Ya Cao, Fei Gao, Dandan Li +1 more

We study protection of a qubit that transfer through a decoherence noise by quantum control technique. In this work, we assume that the communication participants have some side information about the qubit. Our aim is to take fully advantage of given side information to design a quantum control scheme that makes the output state close to the input state as better as possible. Especially, in this paper, we consider the quantum composite control (QCC) structure, which has shown to capture a better balance between fidelity and success probability, i.e., two essential measures for protection. Comparison has been made between our scheme and previous ones. We show there's advantages in two aspects. On one hand, when compared with the scheme that has taking fully consideration of classical side information but not quantum one, our scheme achieves higher fidelity. Inversely, when the scheme with quantum side information but not classical one is considered, our scheme also has nontrivial improvement.