Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the entanglement-assisted classical capacity for any channel is additive, making entanglement across channel uses unnecessary. If the entanglement assistance is limited, the picture is much more unclear. Suppose the classical capacity is superadditive, then the classical capacity with limited entanglement assistance could retain superadditivity by continuity arguments. If the classical capacity is additive, it is unknown if superadditivity can still be developed with limited entanglement assistance. We show this is possible, by providing an example. We construct a channel for which, the classical capacity is additive, but that with limited entanglement assistance can be superadditive. This shows entanglement plays a weird role in communication and we still understand very little about it.Comment: 13 page

Superadditivity in trade-off capacities of quantum channels

In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we want to optimally use a quantum channel for general communication purpose. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity, and it is largely unknown if this could lead to an superadditive double or triple resource capacity. For example, if a channel has an additive classical and quantum capacity, can the classical-quantum capacity be superadditive? In this work, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple capacity region.Comment: 15 pages. v2: typo correcte

Exclusion zone phenomena in water -- a critical review of experimental findings and theories

The existence of the exclusion zone (EZ), a layer of water in which plastic microspheres are repelled from hydrophilic surfaces, has now been independently demonstrated by several groups. A better understanding of the mechanisms which generate EZs would help with understanding the possible importance of EZs in biology and in engineering applications such as filtration and microfluidics. Here we review the experimental evidence for EZ phenomena in water and the major theories that have been proposed. We review experimental results from birefringence, neutron radiography, nuclear magnetic resonance, and other studies. Pollack and others have theorized that water in the EZ exists has a different structure than bulk water, and that this accounts for the EZ. We present several alternative explanations for EZs and argue that Schurr's theory based on diffusiophoresis presents a compelling alternative explanation for the core EZ phenomenon. Among other things, Schurr's theory makes predictions about the growth of the EZ with time which have been confirmed by Florea et al. and others. We also touch on several possible confounding factors that make experimentation on EZs difficult, such as charged surface groups, dissolved solutes, and adsorbed nanobubbles.Comment: 14 pg

Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver’s preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a “witness.” Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender’s signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack’s information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.United States. Air Force. Office of Scientific Research (Grant FA9550-14-1-0052)Massachusetts Institute of Technology. Research Laboratory of Electronics (Claude E. Shannon Fellowship)National Science Foundation (U.S.) (Grant CCF-1525130)National Science Foundation (U.S.) (Center for Science of Information. Grant CCF0-939370