Signifying the nonlocality of NOON states using Einstein-Podolsky-Rosen steering inequalities

Abstract

We construct Einstein-Podolsky-Rosen (EPR) steering signatures for the nonlocality of the entangled superposition state described by 1 √ 2 {|N |0 + |0 |N }, called the two-mode NOON state. The signatures are a violation of an EPR steering inequality based on an uncertainty relation. The violation confirms an EPR steering between the two modes and involves certification of an intermode correlation for number, as well as quadrature phase amplitude measurements. We also explain how the signatures certify an N th order quantum coherence, so the system (for larger N ) can be signified to be in a superposition of states distinct by a mesoscopic value of the two-mode quantum number difference. Finally, we examine the limitations imposed for lossy scenarios, discussing how experimental realisations may be possible for N = 2, 3.

Applications of EPR steering in quantum teleportation and NOON states

“…Wiseman et al [9] proposed EPR steering as a failure of the statistics based on a local hidden state model (LHS) [9,10,11]. An EPR steering inequality based on the LHS model was derived in [2]. This inequality is:…”

“…We now will show another application of steering in order to obtain steering inequalities for the NOON state [2]. For continuous variable systems it is possible to define a steering parameter that allow us to know whether B is steerable by A.…”

“…These states have been created experimentally [38,39,40,41,42,43] and there are many properties that could be measured, for example non-local properties. The derivation of the steering inequalities is given in [2].…”

“…We are also using the notation that covariances are X, Y = XY − X Y , while variances are X, X = XX − X X ≡ (ΔX) 2 . In this contribution we are going to consider the following example of Gaussian states: the two-mode squeezed state (TMSS) with and without losses.…”

“…There has also been recent work on quantification of steering [17,27,28], monogamy relations [29,30,31], and multipartite steering [18,32]. Recently it has been shown the existence of steering inequalities for NOON states [2]. NOON states [33,34,35] are an example of a Schrödinger cat state [36,37], which is an entangled state.…”