In high school math or college math, we've all heard of the concept of imaginary numbers, the square root of negative numbers. It, along with real numbers, forms the concept of complex numbers commonly used in mathematics. The term imaginary number was coined by the famous mathematician Descartes, who at first thought that imaginary numbers were illusory and meaningless. But as mathematical research progressed, scientists found that the introduction of imaginary numbers could make mathematics a powerful tool for dealing with complex physics problems.
In electromagnetism, for example, imaginary or complex numbers greatly simplify the description of wave phenomena. However, many scientists insist that complex numbers are not needed in physical theory, because all meaningful visibles can be represented by real numbers, and complex numbers were introduced only to make calculations easier.
But the concept of complex numbers seems to have been woven into the structure of quantum mechanics when quantum mechanics was established, and our formulas for dealing with or understanding most quantum mechanical problems cannot escape the shadow of complex numbers, and although complex numbers appear only in theoretical formulas, all possible measurements are real numbers.
Whether complex numbers are directly related to the physical significance of quantum mechanics or are merely a computational tool is widely debated. For this reason, many scholars have tried to avoid the concept of complex numbers and create pure real numbers to describe quantum mechanics.
The "real" and "complex" controversy of quantum mechanics
So what is the difference between standard complex number subon theory and real number subon theory? If electrons can only appear in two different positions, quantum theory holds that electrons are in a "superposition state" of two positions, as mysterious as Schrödinger's "cat", which can be represented as a point in abstract two-dimensional Hilbert space and relate the space to the real world through a complex number that calculates the probability of finding the electron in the real position.
The theory proves that if a two-dimensional real numbers are set aside the complex numbers to describe space, it is impossible to describe all the quantum behavior of electrons, but the four-dimensional hilbert space can describe the full probability of the appearance of electrons by doubling the dimensions, which means that quantum mechanics can be represented by real number space.
For the "real" and "complex" controversy of quantum mechanics, a paper by marc-Olivier Renou, a theoretical physicist from the University of Geneva in Spain, published in Nature in December 2021, Quantumtheory based on real numbers can be experimentally falsified He was the first to propose a new theoretical model of Bell experiments to prove that it is insufficient to describe quantum mechanical phenomena only with real-space descriptions.
The New Bell experiment opened up a new path
This new Bell experimental principle is shown in the figure below, two sets of EPR entangled quantum pairs are distributed to three receivers A, B and C, one group is assigned to A and B, and the other group is assigned to B and C, through the EPR entanglement quantum pairs of different quantum operation behaviors, A and C can use their respective methods to dock the received quantum state to measure, B receives from one of the two EPR components of the combined Bell state and measures it, this experiment is like a competition, and finally pass ABC Combining qubit manipulation behavior and comparing the measurement results with each other yields a "score".
Real number subunit theory without imaginary numbers and standard complex quantifier theory will get different "scores" under the conditions, and the "fraction" level makes it possible to judge which one is described correctly.
Figure | New Schematics of bell experiments (Source: Physical Review Letters)
However, the method was not verified by corresponding experiments at that time, and recently the team of Pan Jianwei from the University of Science and Technology of China and the team of Fan Jingyun of southern University of Science and Technology conducted a new Bell experiment verification for the experimental protocol using superconducting quantum and light quantum respectively, and they all proved that the experiment "score" under complex space quantum mechanics was higher, 43 and 4.7 standard deviations higher than that of real space quantum theory, and the relevant results were published in the authoritative journal Physics Review on the same day in January 2022 Letters and get editorial recommendations and news tracking reports.
Ingenious experimental design based on a superconducting quantum computer
Here, we take the superconducting quantum experimental scheme proposed by the team of academician Pan Jianwei of the University of Science and Technology of China as an example. The prototype of the superconducting quantum computer used in the experiment is shown in the figure, the receiver ABC receives four independent qubits from two EPR sources, A receives qubit 1 to get test data a, B receives qubits 2 and 3 gets test data b1 and b2 gets BSM, and C receives qubit 4 to get test data C. Dual qubit control logic is the use of iSWAP gates, while single qubit gates perform different quantum manipulation of qubits along the X, Y, and Z axes. Among them, there are three kinds of manipulation of A = x=1, 2, 3, 3, 5, 6, and the manipulation of C is z=1, 2,3,4,5,6, and the obtained test data is 0 or 1, and the "score" prediction is obtained by the theoretical formula.
Figure | Structure diagram of experimental schemes based on superconducting quanta (Source: Physical Review Letters)
Academician Pan Jianwei of the University of Science and Technology of China realized the production of qubit capacitors, output resonators and transmission lines by using a 100nm aluminum film combined with laser lithography and wet etching on the sapphire substrate. As shown in the figure, the device contains 8 qubits, and the experiment uses four qubits from the second to fifth qubits, each of which is coupled to a transmission capacitive line and a transmission electrical induction line (indicated in red). Each qubit has a separate resonator for the output of the measured data and is coupled to the same output transmission line (indicated in yellow).
Figure | Schematic of a superconducting quantum computer with 8 qubits (Credit: Physical Review Letters)
Through a series of quantum operations and output state readings by the above experimental apparatus, through 12 different manipulation combinations and obtained 16 different qubit data, the joint probability distribution and the "fraction" bit under the standard complex number theory 8.09 can be obtained, which is 43 standard deviations higher than the "score" obtained by the real number of electron theory alone, of which the standard deviation selection is 0.01, which strongly proves the unreliability of the real number of electron theory.
Figure | Obtaining the "score" table of the new Bell experiment in different quantum methods by superconducting quantum computing scheme (Source: Physical Review Letters)
Academician Pan Jianwei of the University of Science and Technology of China has been committed to the research of quantum information and quantum entanglement theory this year, and this time took the lead in exquisitely proving the versatility of complex form quantum theory through superconducting quantum computers, as Professor Alessio Avella of the National Institute of Metrology in Italy commented that this ingenious experiment not only provides a new proof, but also proves that the test technology of new quantum technology can provide better support for quantum basic research. These new insights into quantum mechanics may also have unexpected implications for new quantum information technology developments.
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reference:
1.Renou, MO., Trillo, D., Weilenmann, M. et al. Quantum theory based on real numbers can be experimentally falsified. Nature600, 625–629 (2021).
2.Chen M C, Wang C, Liu F M, et al. Ruling outreal-valued standard formalism of quantum theory[J]. Physical Review Letters,2022, 128(4): 040403.
3.Li Z D, Mao Y L, Weilenmann M, et al. Testingreal quantum theory in an optical quantum network[J]. Physical Review Letters,2022, 128(4): 040402.
4.https://physics.aps.org/articles/v15/7