Hybrid quantum network design against unauthorized secret-key generation, and its memory cost

Abstract

A significant number of servers that constitute the Internet are to provide private data via private communication channels to mutually anonymous registered users. Such are the servers of banks, hospitals that provide cloud storage and many others. Replacing communication channels by maximally entangled states is a promising idea for the quantum-secured Internet (QI). While it is an important idea for large distances secure communication, for the case of the mentioned class of servers pure entanglement based solution is not only unnecessary but also opens a threat. A crack stimulating a node to generate secure connections via entanglement swapping between two hackers can cause uncontrolled consumption of resources. Turning into positive a recently proven no-go result by S. Bäuml et al. [Nat. Commun. 6, 6908 (2015)], we propose a natural countermeasure against this threat. The solution bases on connections between hub-nodes and end-users realized with states that contain secure key but do not allow for swapping of this key. We then focus on the study of the quantum memory cost of such a scheme and prove a fundamental lower bound on its memory overhead. In particular, we show that to avoid the possibility of entanglement swapping, it is necessary to store at least twice as much memory than it is the case in standard quantum-repeater-based network design. For schemes employing either states with positive partial transposition that approximates certain privates states or private states hardly distinguishable from their attacked versions, we derive much tighter lower bounds on required memory. Our considerations yield upper bounds on a two-way repeater rate for states with positive partial transposition (PPT), which approximates strictly irreducible private states. As a byproduct, we provide a lower bound on the trace distance between PPT and private states, shown previously only for private bits.

Attacking the Quantum Internet

“…Message rerouting would work as malicious entanglement and may result in inserting incorrect quantum states, thus affecting Integrity and Availability. In a particular configuration of the network, using bounded entanglement state (or low distillation state) we can resist such an attack [95].…”

Upper bounds on the leakage of private data and operational approach to markovianity

“…A motivation for this and the next Section is given by the fact, that certain private states, as well as states with positive partial transposition that approximate them, are candidates for the hybrid quantum network design [19]. This design ensures that unauthorised key generation will be impossible in quantum networks.…”

“…Below we provide such a construction, based on the Calderbank-Shore-Stean (CSS) codes. On the other hand, the private states, allowing to build the hybrid quantum network [19], should have negligible distillable entanglement. Unfortunately, as we show, the CSS-based construction of private states leads to the states with non-vanishing amount of distillable entanglement (see Proposition 3).…”

“…Attacks on private states. It has been recently proposed [19] that certain private states can serve as a resource for the so called hybrid quantum networks(a variant of quantum network secure against unauthorised key generation). Therefore, we also study special attacks on a particular class of private states.…”

“…Namely, the resulting private state has at least ≈ 0.415 of distillable entanglement. In turn, it can not serve as a building block (see Proposition 3) for the hybrid quantum networks [19].…”