Channel activation of CHSH nonlocality

Abstract

Quantum channels that break CHSH nonlocality on all input states are known as CHSH-breaking channels. In quantum networks, such channels are useless for distributing correlations that can violate the CHSH Inequality. Motivated by previous work on activation of nonlocality in quantum states, here we demonstrate an analogous activation of CHSH-breaking channels. That is, we show that certain pairs of CHSH-breaking channels are no longer CHSH-breaking when used in combination. We find that this type of activation can emerge in both uni-directional and bi-directional communication scenarios.

Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations

“…For example, the hidden nonmacrorealism can be observed up to v max = 0.83 if D ≈ 0.99, which can be achieved by using more glass windows at the Brewster angles. We also note that v = 0.5 is the upper bound of the existence of a CHSH breaking channel [68]. Therefore, our experimental observation implies that the amplitudedamping channel is not a strongly CHSH-nonlocalitybreaking channel [58] for 0.5 < v ≤ 0.64.…”

“…( 4) with arbitrary measurement sets {M a|x } and {M b|y }. Such a channel is called a CHSH nonlocality-breaking channel [58,68]. Now, if the evolved state (1 1 ⊗ E)ρ AB does not show the hidden CHSH nonlocality after applying stochastic local operations with classical communication described by the success quantum-instruments Λ A and Λ B , the channel can be further denoted as a strongly CHSH nonlocality-breaking channel.…”

Quantifying Quantumness of Channels Without Entanglement

“…For the temporal steering and CHSH scenarios, the vanishing parameters v of the SB-breaking and CHSH-breaking channels in the quantum domain are v = 1/ √ 3 and 1/ √ 2, respectively. We note that the temporal CHSH inequality is 0, when v ≤ 1/ √ 2 which is identical to the boundary of the CHSHbreaking channel under the 2-dimensional depolarizing channel [35,62]. Moreover, the vanishing parameter for temporal steerability under the three measurement setting scenario is identical to that in the 3-incompatibility-breaking channel, which breaks the incompatibility of every collection of three measurements [37].…”

“…The quantum bound of the CHSH inequality is given by 2 √ 2. Unlike the situation in the EB scenario, the input of the maximally entangled state is not sufficient for verifying if the channel is CHSH-breaking [35,62]. In this work, we are particularly interested in CHSH-breaking channels with the input being the maximally entangled state, denoted as CHSH-breaking channels for the maximally entangled state, since there are two important properties of such channels: (1) if the marginal of the input state is maximally mixed, then the state after channel cannot violate CHSH inequality and (2) if the channel is unital, then the channel is CHSH-breaking.…”

“…where ρA0 = Tr B0 [ρ A0,B0 ] is the Alice's reduced state. It has been shown that when v ≤ 1 2 , the erasure channel is CHSHbreaking [62]. While the erasure channel is always steerable when v = 0 [51,82] even using only two measurement settings [51,82].…”