Universal Limitations on Quantum Key Distribution over a Network

Abstract

Entanglement is an intriguing quantum phenomenon with crucial implications for both fundamental physics and technological applications, e.g., quantum key distribution (QKD). In this paper, we show that multipartite private states from which secret keys are directly accessible to trusted partners are genuinely multipartite entangled states. With application to secure Quantum Internet, we consider the most general setup of multipartite quantum process (channel) in a network setting: multiplex quantum channel with involved parties having one of the three possible roles-that of only sender or receiver, or both sender and receiver. We derive divergence-based measures for entangling abilities of multipartite quantum channels. We describe an LOCC-assisted secret key agreement (SKA) protocol for generation or distillation of key (private random bits) among multiple trusted allies connected through a quantum multiplex channel secure against a quantum eavesdropper, of which measurement-device-independent QKD and SKA protocols over quantum network laced with key repeaters are particular instances. We are able to provide upper bounds on the non-asymptotic private capacities, maximum rate at which secret key can be distilled via finite uses of channels, and lower bounds on asymptotic capacities. These bounds are expressed in terms of the divergence-based entanglement measures of the channels. Some of these measures lead to strong converse bounds on private capacities. Our upper bounds on the private capacities also are upper bound on the multipartite quantum capacities where goal is to distill Greenberger-Horne-Zeilinger (GHZ) state. Also, we are able to derive upper bound on the secret key bits that can be distilled via LOCC among trusted allies sharing finite copies of multipartite quantum states.

Upper bounds on device-independent quantum key distribution rates in static and dynamic scenarios

“…On practical side the point-to-point or relay-based QKD were achieved commercially and experimentally (see [Hor21] and references therein). From a theoretical perspective, the limitations in form of upper bounds on the key rate were developed in various device-dependent scenarios [CW04, HHHO09, TGW14, PLOB17, WTB17] (also see [AH09,DBWH19]).…”

Genuine multipartite entanglement of quantum states in the multiple-copy scenario

“…Indeed, if all parties share sufficient bipartite entanglement as to enable perfect teleportation any state of any given local dimension can be obtained from them and they are, therefore, universal resources in the standard paradigm of state manipulation under LOCC. Hence, from a more practical point of view, GME can be seen as a benchmark to produce multipartite quantum states useful for applications (possibly conditioned on further LOCC postprocessing) in the light of [16][17][18]. In fact, from this perspective our result uncovers the possibility in general to produce useful multipartite entanglement by mixing partially separable states, as the work of [20] exemplifies in a particular case in the context of quantum cryptography.…”

“…Indeed, most relevant states for applications-like graph states-are GME and the set of biseparable states is closed under LOCC; thus, this classification is welldefined within the standard paradigm of state manipulation under LOCC and biseparable states are then fundamentally limited for many applications. Actually, it has been shown that GME is in general necessary to achieve maximum sensitivity in quantum metrology [16,17] and to establish a multipartite secret key [18]. Nevertheless, all these considerations only involve the single-copy regime.…”

Differential phase shift quantum secret sharing using a twin field

“…Unfortunately, a majority of prepare-and-measure protocols [20][21][22][23][24][25][26] is vulnerable to the Trojan horse attacks [27,28]. Furthermore, in particular, all proposed QSS protocols will confront the linear rate-distance limitation [29][30][31]. This limitation constricts the key rate and transmission distance of QSS.…”