Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity called the bidirectional max-relative entropy of entanglement. We also derive tighter upper bounds on the capacities of bipartite interactions obeying certain symmetries. Observing that reading of a memory device is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a wiretap memory cell. Given a set of point-to-point quantum wiretap channels, the goal of private reading is for an encoder to form codewords from these channels, in order to establish secret key with a party who controls one input and one output of the channels, while a passive eavesdropper has access to one output of the channels. We derive both lower and upper bounds on the private reading capacities of a wiretap memory cell. We then extend these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to a controlled point-to-point channel, which is a particular kind of bipartite interaction.Comment: v3: 34 pages, 3 figures, accepted for publication in Physical Review

Limitations on Quantum Key Repeaters

A major application of quantum communication is the distribution of entangled particles for use in quantum key distribution (QKD). Due to noise in the communication line, QKD is in practice limited to a distance of a few hundred kilometres, and can only be extended to longer distances by use of a quantum repeater, a device which performs entanglement distillation and quantum teleportation. The existence of noisy entangled states that are undistillable but nevertheless useful for QKD raises the question of the feasibility of a quantum key repeater, which would work beyond the limits of entanglement distillation, hence possibly tolerating higher noise levels than existing protocols. Here we exhibit fundamental limits on such a device in the form of bounds on the rate at which it may extract secure key. As a consequence, we give examples of states suitable for QKD but unsuitable for the most general quantum key repeater protocol.Comment: 11+38 pages, 4 figures, Statements for exact p-bits weakened as non-locking bound on measured relative entropy distance contained an erro

Carbocationic cyclisations and rearrangements in the damascone series

A regio- and stereoselective synthesis of the tertiary chloride 7 is described, involving the Lewis acid catalysed addition of the allyl chloride 6 to isobutene as a key step. Acid catalysed cyclisation of 7 yields the damasconoid compounds 12–15