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arXiv:1006.4991 · Physical Review B

Proposal for a cumulant-based Bell test for mesoscopic junctions

Adam Bednorz, Wolfgang Belzig

Published Mar 17, 2011• 34 citations
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Abstract

The creation and detection of entanglement in solid state electronics is of fundamental importance for quantum information processing. We prove that second-order quantum correlations can be always interpreted classically and propose a general test of entanglement based on the violation of a classically derived inequality for continuous variables by fourth-order quantum correlation functions. Our scheme provides a way to prove the existence of entanglement in a mesoscopic transport setup by measuring higher order cumulants without requiring the additional assumption of a single-charge detection.

DOI
10.1103/physrevb.83.125304

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The creation and detection of entanglement in solid state electronics is of fundamental importance for quantum information processing. We prove that second-order quantum correlations can be always interpreted classically and propose a general test of entanglement based on the violation of a classically derived inequality for continuous variables by fourth-order quantum correlation functions. Our scheme provides a way to prove the existence of entanglement in a mesoscopic transport setup by measuring higher order cumulants without requiring the additional assumption of a single-charge detection.
The impossibility of measuring non-commuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of non-commuting observables in mesoscopic transport experiments, using a quasiprobabilistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters. We further address the creation and detection of entanglement in solid-state electronics, which is of fundamental importance for quantum information processing. We propose a general test of entanglement based on the violation of a classically satisfied inequality for continuous variables by 4th or higher order quantum correlation functions. Our scheme provides a way to prove the existence of entanglement in a mesoscopic transport setup by measuring higher order cumulants without requiring the additional assumption of single charge detection.
The quest for fundamental tests of quantum mechanics is an ongoing effort. We here address the question of what are the lowest possible moments needed to prove quantum nonlocality and noncontextuality without any further assumptions---in particular, without the often assumed dichotomy. We first show that second-order correlations can always be explained by a classical noncontextual local-hidden-variable theory. Similar third-order correlations also cannot violate classical inequalities in general, except for a special state-dependent noncontextuality. However, we show that fourth-order correlations can violate locality and state-independent noncontextuality. Finally we obtain a fourth-order continuous-variable Bell inequality for position and momentum, which can be violated and might be useful in Bell tests, closing all loopholes simultaneously.
A theoretical proposal for testing Bell's inequality in mesoscopic systems is presented. We show that the entanglement of two electron spins can be detected in the spin filter effect in the mesoscopic semiconductor / ferromagnetic semiconductor / semiconductor junction. The current-current correlation function is calculated by use of the quantum scattering theory and we compare it with the local hidden variable theory. We also discuss the influence of an imperfect spin filter and derive the condition to see the violation of Bell's inequality experimentally.
Entanglement is central to quantum physics, yet detecting and exploiting it in non-Gaussian systems remains a major challenge. In continuous variable platforms, standard inseparability criteria based on Gaussian statistics-such as the Duan-Simon criterion-fail when quantum correlations are encoded in higher moments of the field quadratures. Here we introduce a framework for detecting non-Gaussian entanglement using higher-order quadrature cumulants. In the Gaussian limit, the lowest order condition reduces to the Duan criterion, while higher-order violations reveal entanglement inaccessible to second-order methods. We experimentally demonstrate a tomography-free certification of inseparability in photon-subtracted squeezed states of light, where Gaussian witnesses fail despite the presence of entanglement. We further show that such higher-order inseparability enables enhanced quantum teleportation of Wigner negativity as compared to Gaussian protocols. These results identify higher-order cumulants as natural observables for non-Gaussian entanglement and open new routes to harnessing non-Gaussian resources in continuous variable quantum technologies.
Entanglement, viz. the non‐separability of quantum states, is a fundamental prediction of quantum mechanics, which is at odds with the classical perception of reality. Furthermore, it constitutes a resource for quantum computation and quantum communication. Electronic degrees of freedom in nanostructures –in particular the spin –constitute promising candidates to implement quantum information architectures in scalable solid state circuits. In this topical review, we will summarize some efforts to create and detect entanglement in such structures. We concentrate first on entanglement in double quantum dots, since they promise to be viable candidates to produce entanglement by confining electrons to a small interaction region. The quantitative detection of the entanglement through transport measurements can be done via current and noise. Secondly, we concentrate on the creation of spin entanglement at quantum point contacts, which has the advantage that the two electrons are automatically spatially separated. We discuss the possibility of performing a Bell test of non‐local correlations. However, as we will point out, a reliable entanglement detection can be performed by current‐correlation measurements, although they require some trust in the experimental setup. Finally, we present a hierarchy of mesoscopic Bell tests, which could be useful to evaluate theoretical proposals and experimental setups.
The standard entanglement test using the Clauser-Horne-Shimony-Holt inequality is known to fail in mesoscopic junctions at finite temperatures. Since this is due to the bidirectional particle flow, a similar failure is expected to occur in an ac-driven contact. We develop a continuous-variable entanglement test suitable for electrons and holes that are created by the ac drive. At low enough temperatures the generalized Bell inequality is violated in junctions with low conductance or a small number of transport channels and with ac voltages which create few electron-hole pairs per cycle. Our ac-entanglement test depends on the total number of electron-hole pairs and on the distribution of probabilities of pair creations similar to the Fano factor.