Abstract
Secure quantum conferencing refers to a protocol where a number of trusted users generate exactly the same secret key to confidentially broadcast private messages. By a modification of the techniques first introduced in [Pirandola, arXiv:1601.00966], we derive a single-letter upper bound for the maximal rates of secure conferencing in a quantum network with arbitrary topology, where the users are allowed to perform the most powerful local operations assisted by two-way classical communications, and the quantum systems are routed according to the most efficient multipath flooding strategies. More precisely, our analysis allows us to bound the ultimate rates that are achievable by single-message multiple-multicast protocols, where N senders distribute N independent secret keys, and each key is to be shared with an ensemble of M receivers.
Highlights
It is important to stress that this result applies to arbitrary network topologies and arbitrary dimensions of the Hilbert space, finite or infinite
Given a network N, we may consider its simulation [35, 36]. This means that, for any edge (x, y), the quantum channel Exy can be replaced by a simulation Sxy = (Txy, σxy) where an LOCC Txy is applied to a resource state σxy, so that Exy(ρ) = Txy(ρ ⊗ σxy) for any input state
We have studied the ultimate conferencing key rates that are achievable in a multi-hop quantum communication network
Summary
Given a quantum channel E, we can simulate it by means of local operations (LOs) and classical communication (CC), briefly called LOCCs, applied to the input state ρ and a resource state σ. For a tele-covariant E, we may write the simulation E(ρ) = Ttele(ρ ⊗ σE), where Ttele is teleportation and σE := I ⊗ E(Φ) is the Choi matrix of the channel (here Φ denotes a finite-dimensional maximally-entangled state). We write E(ρ) = limμ Ttμele(ρ ⊗ σEμ), where Ttμele is the Braunstein-Kimble teleportation protocol based on a two-mode squeezed vacuum state Φμ with variance parameter μ, and σEμ := I ⊗ E(Φμ) is a sequence of quasi-Choi matrices.
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