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. B\"auml et al. [15], 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.
Highlights
The domain of quantum information processing, which shows how the rules of quantum mechanics can meet the needs of information society [1,2], has reached its maturity in recent years
We provide a lower bound on the trace distance between partial transposition (PPT) and private states, shown previously only for private bits
While proposals for overcoming the implications of such an attack are developed, we focus on a solution which to some extent, prevents it due to laws of physics
Summary
The domain of quantum information processing, which shows how the rules of quantum mechanics can meet the needs of information society [1,2], has reached its maturity in recent years. Certain bound entangled states [16] (from which no pure entanglement can be distilled by local operations and communication [17]) and highly noisy private states [18], has been recently shown, to fit the scheme in case of arbitrary 3-way and one-way classical communication (from the node B to A and C) respectively [15,19] In this manuscript, we propose a general idea of physical protection against malware by presenting a flip side of the presented limitation on quantum repeaters. We provide lower bounds for the memory cost of our secure network schemes (hubs) employing PPT states approximating strictly irreducible private states [26].
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