Barbara M. Terhal, Isaac L. Chuang, et al.
Physical Review A - AMO
Entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbitrary quantum state |ξ〉 can be transmitted at some rate Q through a noisy channel χ without degradation. We prove that an EPP involving one-way classical communication and acting on mixed state M(χ) (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel χ) yields a QECC on χ with rate Q=D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts Formula Presented and Formula Presented that can be locally distilled from it by EPPs using one- and two-way classical communication, respectively, and give an exact expression for E(M) when M is Bell diagonal. While EPPs require classical communication, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way communication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single-error-correcting quantum block code. We prove that iff a QECC results in high fidelity for the case of no error then the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. © 1996 The American Physical Society.
Barbara M. Terhal, Isaac L. Chuang, et al.
Physical Review A - AMO
Jay M. Gambetta, A.D. Córcoles, et al.
Physical Review Letters
David P. DiVincenzo, Debbie W. Leung, et al.
IEEE Trans. Inf. Theory
Guido Burkard, Roger H. Koch, et al.
Physical Review B - CMMP