No 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.

We initiate a systematic study to provide upper bounds on device-independent key, secure against a non-signaling adversary (NSDI), distilled by a wide class of operations, currently used in both quantum and non-signaling device-independent protocols. These operations consist of a direct measurements on the devices followed by Local Operations and Public Communication (MDLOPC). We employ the idea of "squashing" on the secrecy monotones, which provide upper bounds on the key rate in secret key agreement (SKA) scenario, and show that squashed secrecy monotones are the upper bounds on NSDI key. As an important instance, an upper bound on NSDI key rate called "squashed non-locality", has been constructed. It exhibits several important properties, including convexity, monotonicity, additivity on tensor products, and asymptotic continuity. Using this bound, we identify numerically a domain of two binary inputs and two binary outputs non-local devices for which the squashed non-locality is zero, and therefore one can not distill key from them via MDLOPC operations. These are mixtures of Popescu-Rohrlich (PR) and anti-PR box with the weight of PR box less than 80%. This example confirms the intuition that non-locality need not imply secrecy in the non-signaling scenario. The approach is general, describing how to construct other tighter yet possibly less computable upper bounds. Our technique for obtaining upper bounds is based on the non-signaling analog of quantum purification: the complete extension. This extension provides the ultimate eavesdropping power with the minimal consumption of eavesdropper's memory and, as we prove, yields equivalent security conditions as previously known in the literature.

No abstract

Almost every quantum system interacts with a large environment, so the exact quantum mechanical description of its evolution is impossible. One has to resort to approximate description, usually in the form of a master equation. There are at least two basic requirements for such a description: first, it should preserve the positivity of probabilities; second, it should correctly describe the equilibration process for systems coupled to a single thermal bath. Existing two widespread descriptions of evolution fail to satisfy at least one of those conditions. The so-called Davies master equation, while preserving the positivity of probabilities, fails to describe thermalization properly. On the other hand, the Bloch-Redfield master equation violates the first condition, but it correctly describes equilibration, at least for off-diagonal elements for several important scenarios. However, is it possible to have a description of open system dynamics that would share both features? In this paper, we partially resolve this problem in the weak-coupling limit: (i) We provide a general form of the proper thermal equilibrium state (the so-called mean-force state) for an arbitrary open system. (ii) We provide the solution for the steady-state coherences for a whole class of master equations, and in particular, we show that the solution coincides with the mean-force Hamiltonian for the Bloch-Redfield equation. (iii) We consider the cumulant equation, which is explicitly completely positive, and we show that its steady-state coherences are the same as one of the Bloch-Redfield dynamics (and the mean-force state accordingly). (iv) We solve the correction to the diagonal part of the stationary state for a two-level system both for the Bloch-Redfield and cumulant equation, showing that the solution of the cumulant is very close to the mean-force state, whereas the Bloch-Redfield differs significantly.