Ruling Out Real-Valued Standard Formalism of Quantum Theory

Complex Field Formulation of the Quantum Estimation Theory

“…where L z are the complex symmetric logarithmic derivatives of |α , which are implicitly given by (37), that is,…”

“…Recently, the advantages of estimating complex quantities using their native representation has been studied in the case of radio interferometric gain calibration [32] and optimization on complex variables has been applied to signal analysis [33] and neural networks [34,35]. Furthermore, complex numbers have been shown to play a fundamental role in the formulation of quantum mechanics [36,37], that is, a formulation of quantum mechanics on real numbers leads in certain scenarios to different predictions than quantum mechanics formulated on complex numbers. Alternative formulations of estimation theory have been proposed [38,39], where the Fisher information matrix and the Cramér-Rao bound are adapted to consider complex statistics of complex parameters.…”

Probing fundamental aspects of quantum mechanics with quantum computers

“…The standard, complex-based quantum framework yields and ideal score of Γ = 6 √ 2 ≈ 8.49. Two impressive experiments [25,26] have since shown convincing evidence that the traditional formulation of quantum theory does require complex-valued quantities with experimentally obtained values of Γ exceeding Γ crit significantly. The main focus of the remainder of this paper is to demonstrate how the experimental setup in Ref.…”

“…To support the claim that IBM Quantum devices are useful for performing quantum experiments such as Bell tests which are accessible with small systems, particular attention is paid to demonstrating the robustness of the results. One tradeoff of accessing cloud-based, programmable quantum hardware with Qiksit compared to specially-fabricated devices [25] is that one generally loses at least some control over the precise calibration of the device. Evidence is presented to demonstrate the results obtained are robust with respect to IBM's daily calibrations.…”

Quantum Mechanics Must Be Complex

“…However, the possibility of using real numbers was never formally ruled out, and recent theoretical results suggested that a real-valued quantum theory could describe an unexpectedly broad range of quantum systems [2]. But this real-number approach has now been squashed by two independent experiments, performed by Ming-Cheng Chen of the University of Science and Technology of China [3] and by Zheng-Da Li of the Southern University of Science and Technology, China [4]. The two teams show that, within a standard formulation of quantum mechanics, complex numbers are indispensable for describing experiments carried out on simple quantum networks.…”