The Qubit in de Broglie-Bohm Interpretation

Michel Gondran (1) , Alexandre Gondran (2)

1 AEIS - Académie Européenne Interdisciplinaire des Sciences
2 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien

In quantum information, the spin-based qubit is not represented by a whole spinor in space as illustrated by the z spinor below : <> but by a simplified spinor without spatial extension : <> This simplification is the basis of our first remark about the quantum computer concept. Indeed, the demonstrations explaining the interest of the Deutsch, Glover and Shor algorithms are based on calculations using the factorization of entangled qubits. These factorizations are accurate for spinors without spatial extensions, but only approximate for real spinors with spatial extensions. A more fundamental remark concerns the existence of the qubit as a superposition of quantum states. This reality depends on the quantum mechanics interpretation. In the de Broglie-Bohm interpretation, the wave function (spinor) is not sufficient to completely describe the quantum state of a particle ; it is necessary to add the position of the particle. The spinor spatial extension takes into account the initial position of the particle. However, this position is unknown to the experimenter and is revealed only when measuring. Several particles prepared in the same way have the same wave function (spinor) but different positions. In this interpretation, the superposition of states does not really exist for an individual particle. It is only a linear combination of states resulting from our ignorance of the position of the particle. The superposition of states represents only a statistical collection of particles and the spinor corresponds to a statistical qubit. We present a detailed study of the whole spinor evolution (in space and in time) in the Stern and Gerlach experiment and we explain the decoherence, the individual impacts and the quantization. Our analysis explains very simply, in the de Broglie-Bohm interpretation, the negative results of the NMR technique in attempts to make a large quantum computer (more than 7 qubits). This technique does not use individual quantum objects, but a set of more than 10 8 active molecules diluted in a solvent : the measurement is thus a collective and reliable signal. The results of the NMR data being statistical, then we have a natural explanation of the drop by a factor two of the signal strength. Finally, the parallel quantum computer is feasible in the interpretation of Deutsch and the parallel universes of Hug Everett, but impossible in the de Broglie-Bohm interpretation. In this interpretation, the individual qubit does not exist and we must use two particles to represent it ; the statistical qubit alone exists, such as in Chuang’s computer.

Mots clés: Quantum bit

Domaines: Physique Quantique [quant-ph]

Michel Gondran, Alexandre Gondran. The Qubit in de Broglie-Bohm Interpretation. Advances in Quantum Information & Simulations, Nov 2014, Lyon, France. , Book of Abstracts, 2014. ⟨hal-01348981⟩