Limitations on quantum key repeaters

Abstract

A major application of quantum communication is the distribution of entangled particles for use in quantum key distribution. Owing to noise in the communication line, quantum key distribution 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 that performs entanglement distillation and quantum teleportation. The existence of noisy entangled states that are undistillable but nevertheless useful for quantum key distribution 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 quantum key distribution but unsuitable for the most general quantum key repeater protocol.

Inequalities for the quantum privacy

“…The optimal strategy, in order to reverse the action of an arbitrary channel acting on an ensemble of n qudits is optimally reverse the associated Gaussian channel and map the output back onto m qudits. More recently, in a study of long-distance quantum communication and cryptography beyond the use of entanglement distillation, an asymptotic version of the distinguishability bound has been derived by Bauml et al [28].…”

The PPT square conjecture holds generically for some classes of independent states

“…Let d := d 1 = d 2 , if W 1 , W 2 are chosen independently, then the distribution of the random matrix Z defined in(7) converges to the centered Marcheko-Pastur distribution of parameter c 2 (rescalled by the factor c) almost surely as d → ∞, s/d → c.…”

On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states

“…This led to upper bounds on the secure content of quantum states via relative entropy of entanglement [5][6][7] and squashed entanglement [8][9][10][11] and further generalizations for quantum channels via squashed entanglement of a quantum channel [12,13] and relative entropy of entanglement extended to quantum channel [14] (see also [15][16][17][18] in this context). Recently, there has been shown a related impossibility result that one cannot achieve non-negligible amount of key [19] in the framework of quantum repeaters [20] using some certain approximate private states (a problem of quantum key-repeaters).In general the importance of the class of private states follows from the fact that any quantum key distribution protocol (including the so-called quantum device independent ones [21,22]) is equivalent to a OPEN ACCESS RECEIVED…”