Angular-momentum nonclassicality by breaking classical bounds on statistics

Abstract

We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without evaluation of moments, or any other more sophisticated procedures. These nonclassical tests are very general and independent of other typical quantum signatures of nonclassical behavior such as sub-Poissonian statistics, squeezing, or oscillatory statistics, being insensitive to the nonclassical behavior displayed by other variables.

Equivalence of classicality and separability based on P phase-space representation of symmetric multiqubit states

“…as spin coherent states are normalized: θ, φ|θ, φ = 1. However, the P function is not ensured to be a bonafide statistical probability density -and hence it leads to notions of non-classicality of spin states [5,6]. Any arbitrary pure state of a qubit (spin-1/2 system) |ψ = cos(Θ/2) e −iΦ |0 + sin(Θ/2) e iΦ |1 is a spin coherent state as it can always be expressed as a rotated "spin down state" |ψ = R(π − Φ, π + Θ, Φ − π)|1 ≡ |π + Θ, −Φ .…”

“…[5]. Luis and Rivas [6] showed that spin squeezing [7] manifestly reflects the failure of P function to be a classical probability density. Simple operational procedures revealing the violation of classical statistical bounds by spin states endowed * Electronic address: arutth@rediffmail.com with non-classical P representation were also derived in Ref.…”

“…Simple operational procedures revealing the violation of classical statistical bounds by spin states endowed * Electronic address: arutth@rediffmail.com with non-classical P representation were also derived in Ref. [6]. Besides studying the non-classicality of single spin systems, Giraud et.…”

Anticoherence of spin states with point-group symmetries

“…These states, with maximally mixed one-qubit reductions, have been the subject of numerous research [19][20][21][22][23][24][25][26], notably due to their importance in two-party communication tasks. Similarly, the notion of non-classicality of spin states based on the Glauber-Sudarshan P representation [27,28] has been translated to multiqubit symmetric states in [29] where it has been shown to imply entanglement.…”

Atomic nonclassicality quasiprobabilities

“…The creation of entanglement in spin systems [12,13] and the relation between entanglement and squeezing [14] have also been studied. Recently, nonclassicality has been examined in terms of measurable probability distributions [15].…”