Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering

Abstract

I. PROOFSResult ( . Proof: Without loss of generality, we will assume g sym = g, using the definition of g sym we can write Ent B|A and (g 2 sym − 1)/(g 2 sym + 1) as:We wish to prove thatExpanding this expression we notice that it is equivalent to prove that:From the PPT condition nm − c 2 + 1 − n − m > 0, we know that nm > c 2 − 1 + n + m, so we can writeNext, we use that −1 + n + m ≥ 1 + m − n, this inequality holds since we are considering n ≥ 1. Hence we can write:So that in order to prove that Ent ≥ (g 2 sym − 1)/(g 2 sym + 1) we need to prove that:Let us prove this by contradiction, hence we suppose thatThis implies that:⇐⇒ (m + n) 2 ≤ (m − n) 2 + 2 m − n + 2c 2 ⇐⇒ m 2 + 2mn + n 2 ≤ m 2 − 2mn + n 2 + 2m − 2n + 4c 2 ⇐⇒ 4mn ≤ 2m − 2n + 4c 2 ⇐⇒ 2 mn − c 2 ≤ m − n.

No-cloning of quantum steering

“…However, whether such a result can provide a relation in the form of Coffman-Kundu-Wootters monogamy inequality (see, for example, equation (1) in Kay et al 11 ) still needs further investigation. In addition, He et al 13 have shown that two-way steering is required to overcome the no-cloning threshold for secure teleportation. This relationship, between no-cloning and EPR steering, also suggests a principle of no-cloning for the correlations used for teleportation.…”

“…Their quantum information-task-oriented method, to investigate the relationship between the no-cloning theorem and steering, indicates that it may be interesting, in future work, to consider the security threshold for secure quantum teleportation derived from our input-output scenario for cloning quantum steering, and to compare this condition on fidelity with their criterion. 13 Figure 1b, …”

Einstein-Podolsky-Rosen steering and Bell nonlocality of two macroscopic mechanical oscillators in optomechanical systems

“…2 (a)-(b)) that the state with logarithmic negativity E N > ln3 ≈ 1.1 is of two-way steerability. This is valid for any two-mode Gaussian state under Gaussian measurements [40,46]. Fig.…”

Swapping of Gaussian Einstein-Podolsky-Rosen steering

“…EPR steering can be regarded as verifiable entanglement distribution by an untrusted party, while entangled states need both parties to trust each other, and Bell nonlocality is valid assuming that they distrust each other [7]. In the field of quantum information processing, EPR steering has potential applications in onesided device-independent quantum key distribution [9], channel discrimination [10], and teleamplification [11]. * Electronic address: suxl@sxu.edu.cn…”