For quantum information, two wrongs can make a right

Superactivation is the phenomenon where two quantum channels which individually have zero-capacity can have positive capacity when used together. The perspective given here provides an intuitive explanation of this discovery by Smith and Yard, and gives a protocol to activate any private channel

A post-quantum theory of classical gravity?

We present a consistent theory of classical gravity coupled to quantum field theory. The dynamics is linear in the density matrix, completely positive and trace-preserving, and reduces to Einstein's equations in the classical limit. The constraints of general relativity are imposed as a symmetry on the equations of motion. The assumption that gravity is classical necessarily modifies the dynamical laws of quantum mechanics -- the theory must be fundamentally stochastic involving finite sized and probabilistic jumps in space-time and in the quantum field. Nonetheless the quantum state of the system can remain pure conditioned on the classical degrees of freedom. The measurement postulate of quantum mechanics is not needed since the interaction of the quantum degrees of freedom with classical space-time necessarily causes collapse of the wave-function. More generally, we derive a form of classical-quantum dynamics using a non-commuting divergence which has as its limit deterministic classical Hamiltonian evolution, and which doesn't suffer from the pathologies of the semi-classical theory.Comment: "It's very difficult to find a black cat in a dark room, especially if there is no cat.

Hybrid Zero-capacity Channels

There are only two known kinds of zero-capacity channels. The first kind produces entangled states that have positive partial transpose, and the second one - states that are cloneable. We consider the family of 'hybrid' quantum channels, which lies in the intersection of the above classes of channels and investigate its properties. It gives rise to the first explicit examples of the channels, which create bound entangled states that have the property of being cloneable to the arbitrary finite number of parties. Hybrid channels provide the first example of highly cloneable binding entanglement channels, for which known superactivation protocols must fail - superactivation is the effect where two channels each with zero quantum capacity having positive capacity when used together. We give two methods to construct a hybrid channel from any binding entanglement channel. We also find the low-dimensional counterparts of hybrid states - bipartite qubit states which are extendible and possess two-way key

How to reuse a one-time pad and other notes on authentication, encryption and protection of quantum information

Quantum information is a valuable resource which can be encrypted in order to protect it. We consider the size of the one-time pad that is needed to protect quantum information in a number of cases. The situation is dramatically different from the classical case: we prove that one can recycle the one-time pad without compromising security. The protocol for recycling relies on detecting whether eavesdropping has occurred, and further relies on the fact that information contained in the encrypted quantum state cannot be fully accessed. We prove the security of recycling rates when authentication of quantum states is accepted, and when it is rejected. We note that recycling schemes respect a general law of cryptography which we prove relating the size of private keys, sent qubits, and encrypted messages. We discuss applications for encryption of quantum information in light of the resources needed for teleportation. Potential uses include the protection of resources such as entanglement and the memory of quantum computers. We also introduce another application: encrypted secret sharing and find that one can even reuse the private key that is used to encrypt a classical message. In a number of cases, one finds that the amount of private key needed for authentication or protection is smaller than in the general case.Comment: 13 pages, improved rate of recycling proved in the case of rejection of authenticatio

Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime

In this brief note, we compare two frameworks for characterizing possible operations in quantum thermodynamics. One framework considers Thermal Operations---unitaries which conserve energy. The other framework considers all maps which preserve the Gibbs state at a given temperature. Thermal Operations preserve the Gibbs state; hence a natural question which arises is whether the two frameworks are equivalent. Classically, this is true---Gibbs-Preserving Maps are no more powerful than Thermal Operations. Here, we show that this no longer holds in the quantum regime: a Gibbs-Preserving Map can generate coherent superpositions of energy levels while Thermal Operations cannot. This gap has an impact on clarifying a mathematical framework for quantum thermodynamics.Comment: 4 pages, 1 figur

A Resource Theory for Work and Heat

Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilised to describe thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. We apply this resource theory to the case of many non-interacting systems, and show that all quantum states are classified by their entropy and average energy, even arbitrarily far away from equilibrium. This implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs, or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for other resource theories.Comment: main text: 12 pages, 5 figure; appendix: 7 page