I blogged about this article here.
One of the largest one questions in quantum information theory is the additivity of the Holevo capacity of quantum channels. The Holevo capacity of a quantum channel is the rate at which you can send classical information down this channel. The additivity conjecture asserts that using two separate quantum channels N1 and N2 whose Holevo capacities are C1 and C2, that the Holevo capacities of using the two channels used in parallel is C1+C2. Shor showed that this conjecture, along a host of different additivity questions in quantum information, are all equivalent to an additivity conjecture about minimum output entropy. The minimum output entropy of a channel is simply the minimum Shannon entropy which can be produced by feeding this channel a pure state input. The additivity conjecture here is the same as above: that the minimum output entropy of a parallel use of channels adds. One approach that people have pursued to proving this conjecture is, instead of considering the Shannon entropy, to consider Renyi entropies. Renyi entropies are parameterized by a value p, which as p goes to 1 from above approaches the Shannon entropy. The hope was that if one could prove additivity for the minimum Renyi entropy, then one could boost this up to a proof for the more physically relevant Shannon entropy. These hopes have been, over the years, slowly picked away at. This culminated recently with Winter showing that for p>2 that the conjecture did not hold, and then with Hayden showing that for 1>p>2, it also did not hold. The paper here strengthens these two results (the authors discuss the additivity of the maximal p-norm multiplicity conjecture which is simply related to the additivity conjectures for the minimal output entropy. Of particular note is that the authors show that the conterexamples provided by Hayden extend not just to 1>p>2, but to p>1.
In the Unruh effect, an accelerating observer, sees a vacuum state which is a thermal state. Here the authors consider how this effect can be used to communicate privately. Here is the setting: suppose that you and your friend are in inertial frames and want to talk privately. Luckily for you, the eavesdropper who you don’t want to listen in on your conversation is in an accelerating frame. This means that, from the perspective of the eavesdropper, communication between you and your friend appears to be noisy due to the Unruh effect. This noise can then be used to hide information from the eavesdropper. In this paper the authors consider this scenario for private classical and private quantum communication. The former they obtain an explicit lower bound for the private classical capacity of the Unruh channel and show that this capacity is nonzero. For the later they show that the private quantum capacity is zero. A gem of an acknowledgment “The authors thank John Preskill for reminding us of the dangers of preliminary calculations…” A question: does this work for two accelerating observors with respect to an inertial eavesdropper? Another question: Suppose that two parties share a secret acceleration plan can they used this to then securely transmit against all other observers?
Suppose that you want to carry out a quantum computation on a quantum computer, but, because a three letter agency owns and operates that quantum computer, you aren’t exactly thrilled at letting that agency know what you are computing. Is it possible for you to interactively send instructions to this quantum computer, such that the local operator of that quantum computer cannot figure out what you are computing: i.e. it cannot figure out your input, quantum computation, and output? Further is it possible to do this in such a way that you can detect when the quantum computer operator is being malicious? The authors of this paper present a protocol for achieving this. Notably this paper beats what has been known previously: Childs showed how to perform private computation but without the ability to detect an interfering quantum computer and Arrighi and Salvai showed how to perform private computation but for a limited class of functions (not polynomial sized quantum circuits) and with a detection probability polynomial in the circuit size. Here the authors claim to have made the detection probability exponential in the circuit size, while also only working with polynomial sized quantum circuits. Notably their protocol uses no quantum memory for the person performing the quantum computation, but only the ability to produce single qubit states (though there is an implicit notion of memory being used in that the party is assumed to be able to transmit these states perfectly to the computer.) The scheme relies on measurement based quantum computing.
Other papers receiving significant scitations:
0807.4797 (5 scites) “Transitions in the computational power of thermal states for measurement-based quantum computation” by Sean D. Barrett, Stephen D. Bartlett, Andrew C. Doherty, David Jennings, and Terry Rudolph