Classical limits and contextuality in a scenario of multiple observers

Roberto D. Baldijão and Marcelo Terra Cunha

Phys. Rev. A 102, 052226 – Published 30 November 2020

Abstract

Contextuality is regarded as a nonclassical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over classical analogs. In our work, we adapt the $N$ -cycle scenarios with odd $N$ to multiple independent observers which measure the system sequentially. We analyze the possibility of violating the inequalities as a function of the number of observers and under different measurement protocols. We then reinterpret the results as an open quantum system where the environment is divided into fragments. In this context, the results show the emergence of noncontextuality in such a setting, bringing together the quantum behavior to our classical experience. We then compare such emergence of noncontextuality with that of objectivity under the “environment as a witness” paradigm.

Received 4 August 2020
Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevA.102.052226

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum correlations in quantum information Quantum correlations, foundations & formalism Quantum foundations Quantum measurements Quantum-to-classical transition

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Roberto D. Baldijão ^1,2,* and Marcelo Terra Cunha ³

¹Institute of Physics “Gleb Wataghin”, State University of Campinas, 13083-859 Campinas, SP, Brazil
²Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
³Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil

^*Corresponding author: rdbaldi@ifi.unicamp.br

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Issue

Vol. 102, Iss. 5 — November 2020

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Images

Figure 1
Hypergraph representing a five-cycle realization in a theory obeying $p (- 1, - 1 | i, i + 1) = 0$ . Hyperedges represent each context ${A_{i}, A_{i + 1}}$ . The $a_{i}$ vertices denote the outcomes “yes” to the related effects, important for expression $α$ (hence the continuous line) and the $b_{i}$ vertices are “yes” answers to the related effects, where the dashed line reinforce its exclusiveness only to ${a_{i}, a_{i + 1}}$ . Nondisturbance in this dichotomic scenario, or the validity of the “Gleason property” for the effects, allows us to consider $a_{i}$ “the same” vertex for both hyperedges it belongs to (see Appendix pp1). Noncontextuality to deterministic assignments then implies Inequalities (6).
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Figure 2
Scheme for the multiplayers game. (a) First player makes a measurement $i_{1}$ on state $ρ$ , obtaining his outcome $o_{i_{1}} | i_{1}$ . All other players ignores $i_{1}$ and $o_{i_{1}}$ . (b) Second player makes a measurement on state $σ$ which depends on $ρ$ , $i_{1}$ and $o_{i_{1}} | i_{1}$ , and so on.
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Figure 3
(a) Minimum value of $β_{Q}^{k}$ for the $k th$ player, for protocols 1 (black) and 3 (red). (b) Maximum value of $α_{Q}^{k}$ for the $k th$ player for measurement protocols 1 (black) and 2 (red). Initial state is $| ψ_{handle} 〉$ and $N = 9$ . Blue line sets the quantum highest violation and Green line sets the noncontextual bounds.
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Figure 4
We can interpret each measurement on the sequential setup as a strong interaction in a collisional approach. In each interaction (e.g., with $E_{1}$ ), an observable is monitored on $S$ and such information is transfered to the environmental fragment through the correlations established by the interaction; i.e., it can be recovered by measuring $ρ_{E_{1}}^{'}$ . The decohered $S$ then interacts with the next system, e.g., $E_{2}$ and so on.
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Figure 5
(a) Two hyperedges defining joint measurements with its initially four outcomes. (b) ND says that the probabilities assinged to the upper (lower) events on either hyperedge must sum up to the same value. This can be used together with normalization condition for each hyperedge to obtain that probabilities assinged to the events in the green hyperedges must sum up to one. (c) Exclusiveness essentialy allows to take $(- 1 - 1 | i, j)$ out of consideration, implying the operation equivalence of these two vertices and the outcome of the measurement of $A_{0}$ alone. (d) The operational equivalence allows to identify these events as one vertex and we end up with this new hypergraph for these contexts.
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