On the complementary quantum capacity of the depolarizing channel

The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity for all $\eta>0$. Thus, we find that there exists a single parameter family of channels having the peculiar property of having positive quantum capacity even when the outputs of these channels approach a fixed state independent of the input. Comparisons with other related channels, and implications on the difficulty of studying the quantum capacity of the depolarizing channel are discussed.Comment: v4 corrects errors in equation (38

Maximal Privacy Without Coherence

Privacy lies at the fundament of quantum mechanics. A coherently transmitted quantum state is inherently private. Remarkably, coherent quantum communication is not a prerequisite for privacy: there are quantum channels that are too noisy to transmit any quantum information reliably that can nevertheless send private classical information. Here, we ask how much private classical information a channel can transmit if it has little quantum capacity. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.Comment: 6 pages. Proof of Eq.(13) slightly revise

Why is Polygyny More Prevalent in Western Africa?: An African Slave Trade Perspective

Polygyny rates are higher in Western Africa than in Eastern Africa. The African slave trades explain this difference. More male slaves were exported in the trans-Atlantic slave trades from Western Africa, while more female slaves were exported in the Indian Ocean and Red Sea slave trades from Eastern Africa. The slave trades led to prolonged periods of abnormal sex ratios, which impacted the rates of polygyny across Africa. In order to assess these claims, we construct a unique ethnicity-level data set linking current rates of polygyny with historical trade flow data from the African slave trades. Our OLS estimates show a positive correlation between the trans-Atlantic slave trades and polygyny. An IV approach shows the relationship is causal and statistically signicant. We also provide cross-country evidence corroborating our findings.slave trades; polygyny; Africa; development

The Medicare Physician Group Practice Demonstration: Lessons Learned on Improving Quality and Efficiency in Health Care

Discusses the experiences of ten large practices earning performance payments for improving the quality and cost-efficiency of health care delivered to Medicare fee-for-service beneficiaries