Almost i.i.d. sources and the robustness of entanglement distillation

Speaker: Nilanjana Datta (University of Cambridge)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

Many foundational results of quantum information theory were established under the assumption that sources, channels and entanglement resources are independent and identically distributed (i.i.d.) and rely on the resulting quantum typicality. However, which features of this i.i.d. framework are actually essential? A remarkably general class of sequences of multipartite quantum states satisfying a weak form of the i.i.d. property is considered: their fixed-size marginals converge, on average, to those of a reference i.i.d. source, while allowing arbitrary global correlations and entanglement. We prove that these almost i.i.d. sources nevertheless satisfy two fundamental concentration principles: a noncommutative weak law of large numbers and a universal entropy-concentration theorem. These results show that entropy concentration suffices for many manifestations of quantum typicality even when approximate equipartition fails.

These concentration principles lead to a unified perspective on the robustness of a range of information-theoretic tasks beyond the i.i.d. setting, including entanglement distillation, which will be the focus of this talk. Combining the weak law of large numbers with quantum error correction, we show that, under either one-way or two-way classical communication, every rate below the corresponding i.i.d. distillable entanglement of the reference state is achievable by a single sequence of entanglement-distillation protocols for all almost i.i.d. sources along that reference state.

The entanglement-distillation results are joint work with Ryuji Takagi.