Quantum theory based on real numbers can be experimentally falsified

Abstract

While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through theories. While most theories of physics are based on real numbers, quantum theory was the first to be formulated in terms of operators acting on complex Hilbert spaces. This has puzzled countless physicists, including the fathers of the theory, for whom a real version of quantum theory, in terms of real operators, seemed much more natural. In fact, previous works showed that such "real quantum theory" can reproduce the outcomes of any multipartite experiment, as long as the parts share arbitrary real quantum states. Thus, are complex numbers really needed in the quantum formalism? Here, we show this to be case by proving that real and complex quantum theory make different predictions in network scenarios comprising independent states and measurements. This allows us to devise a Bell-like experiment whose successful realization would disprove real quantum theory, in the same way as standard Bell experiments disproved local physics.

21 pages. Some typos corrected in the analytic proof, new discussion about the use of tensor products to model space-like separation in quantum field theory, short introduction to non-local real quantum models reproducing the predictions of quantum theory, compendium of theoretical arguments against real quantum theory, real quantum simulation of joint measurements of independent preparations

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Cited by in corpus (97)

• Bell nonlocality in networks
• Testing real quantum theory in an optical quantum network
• Ruling out real-valued standard formalism of quantum theory
• Full network nonlocality
• Entanglement swapping and quantum correlations via Elegant Joint Measurements
• Semidefinite programming relaxations for quantum correlations
• Quantum networks self-test all entangled states
• Experimental refutation of real-valued quantum mechanics under strict locality conditions
• Real quantum operations and state transformations
• Unitary-invariant witnesses of quantum imaginarity
• Resource Theory of Imaginarity: New Distributed Scenarios
• Complex networks with complex weights
• Nonlocality for Generic Networks
• Quantum Correlations in the Minimal Scenario
• Proofs of network quantum nonlocality in continuous families of distributions
• Imaginarity of Gaussian states
• Quantifying the imaginarity of quantum states via Tsallis relative entropy
• Is there a finite complete set of monotones in any quantum resource theory?
• Certification of non-classicality in all links of a photonic star network without assuming quantum mechanics
• Positive maps and entanglement in real Hilbert spaces
• Source-independent quantum random number generator against tailored detector blinding attacks
• Network nonlocality sharing via weak measurements in the extended bilocal scenario
• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Nonlocal Advantages of Quantum Imaginarity
• Network Nonlocality via Rigidity of Token-Counting and Color-Matching
• Sharing nonlocality in quantum network by unbounded sequential observers
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Optimal discrimination between real and complex quantum theories
• Quantum violation of local causality in urban network with hybrid photonic technologies
• How many mutually unbiased bases are needed to detect bound entangled states?
• Quantum-state texture and gate identification
• Quantifying imaginarity in terms of pure-state imaginarity
• Hierarchical certification of nonclassical network correlations
• Proposals for ruling out the real quantum theories in an entanglement-swapping quantum network with causally independent sources
• Correspondence between entangled states and entangled bases under local transformations
• Post-quantum nonlocality in the minimal triangle scenario
• Geometric-Like imaginarity: quantification and state conversion
• Coherence and imaginarity of quantum states
• Expectation value dynamics within real Hilbert space quantum mechanics
• All Real Projective Measurements Can be Self-tested
• Efficient discrimination between real and complex quantum theories
• Generalized dynamical theories in phase space and the hydrogen atom
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Geometry of sets of Bargmann invariants
• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation
• Quantum mechanics based on real numbers: A consistent description
• Partial independence suffices to rule out Real Quantum Theory experimentally
• $(n,m,p)$-type quantum network configuration and its nonlocality
• Two convergent NPA-like hierarchies for the quantum bilocal scenario
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantifying the imaginarity via different distance measures
• Nonlocal correlations in an asymmetric quantum network
• Galilean relativity and wave-particle duality imply the Schrödinger equation
• Memory attacks in network nonlocality and self-testing
• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• Spin Vector Potential and Spin Aharonov-Bohm Effect
• Multi-Path and Multi-Particle Tests of Complex vs. Hyper-Complex Quantum Theory
• Quantifying the phase of quantum states
• Imaginarity measures induced by real part states and the complementarity relations
• Quantifying imaginarity of quantum operations
• Revisiting Schrodinger's fourth-order, real-valued wave equation and its implications to energy levels
• Quantum correlations cannot be reproduced with a finite number of measurements in any no-signaling theory
• Klein-Gordon equation within the real Hilbert space formalism
• Self-interacting quantum particles and the Dirac delta potential
• Analyzing the free states of one quantum resource theory as resource states of another
• Beyond the Projection Postulate and Back: Quantum Theories with Generalised State-Update Rules
• Generalized Probabilistic Theories in a New Light
• Newton's laws of motion generating gravity-mediated entanglement
• Certifying asymmetry in the configuration of three qubits
• Strict advantage of complex quantum theory in a communication task
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• An Elementary Characterization of Bargmann Invariants
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• The detection power of real entanglement witnesses under local unitary equivalence
• Testing the necessity of complex numbers in traditional quantum theory with quantum computers
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• Quantum non-classicality in the simplest causal network
• Toward Quantum-Aware Machine Learning: Improved Prediction of Quantum Dissipative Dynamics via Complex Valued Neural Networks
• Detecting quantum resources in a semi-device independent framework
• Experimental genuine quantum nonlocality in the triangle network
• Gleason's Theorem for a Qubit as Part of a Composite System
• Faithful real embedding of a three-dimensional complex Kochen-Specker configuration
• Deformed angular momentum algebra within the real Hilbert space
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Entanglement concentration via measurement:- role of imaginarity
• Markovian dynamics of single-rebit open quantum systems with applications to colour perception
• Causal influence versus signalling for interacting quantum channels
• The quantum harmonic oscillator and the real Hilbert space
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• A New Perspective on Quantum Field Theory Revealing Possible Existence of Another Kind of Fermions Forming Dark Matter
• Generalized imaginary units in quantum mechanics
• Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de Finetti theorems
• Robust self-testing and certified randomness based on chained Bell inequality
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Semi-device-independent certification of number of measurements