Biologische Korrelate

Distribution of continuous-variable entanglement by separable Gaussian states

“…Remarkably, one can entangle two distant modes by a separable mode using experimentally feasible Gaussian states and operations involving single-mode squeezed states, correlated displacements and beam splitters, dispensing with the CNOT gates of the qubit case. The distributed entanglement is distillable [20] and therefore can be used for quantum communication. In contrast with two qubits, two light modes can be entangled deterministically even without any additional operation on Bob's system and ancilla beyond step 3 (cf.…”

Quantum Key Distillation from Gaussian States by Gaussian Operations

“…[15,16]: quantum distillation by Gaussian operations is impossible. That is, although it is known that all Gaussian states with non-positive partial transposition (NPPT) are distillable [17], any distillation protocol must include a non-Gaussian operation. This can be rephrased saying that all entangled mixed states are bound entangled in the Gaussian scenario.…”

“…The PPT criterion provides a necessary and sufficient condition for separability for 1 × 1 [21] and 1 × N Gaussian states [22], while it is only a necessary condition for the rest of systems [22]. As said above, the non-positivity of the partial transposition is a necessary and sufficient condition for distillability [17].…”

“…Two known results will play an important role in what follows. First, any NPPT Gaussian state of n + m modes can be mapped by GLOCC into an NPPT 1 × 1 Gaussian and symmetric state [17], whose CM, see Eq. (3), is…”

“…Since all the NPPT Gaussian states can be mapped into symmetric and entangled states of two modes by GLOCC, we restrict our analysis to this type of states. In equivalent terms, one can think that the first step in the key distillation protocol is the GLOCC transformation of [17] that transforms any NPPT state into an entangled state of this family. Then, both parties measure the X quadrature, where X A and X B denote the measured operator and x A and x B the obtained outcome.…”