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arXiv:2210.06045 · Physical Review A

Multiple measurements on an uncollapsed entangled two-photon state

Dalibor Javůrek

Published Aug 10, 2023• 1 citation
arXivHTMLPDF

Abstract

The relativity of simultaneity together with the definition of a quantum state collapse results in experimental situations where multiple measurements can be taken on an uncollapsed quantum state. The quantum state's collapse is defined to be instantaneous in a rest inertial frame of a detector performing measurements on the quantum system. The definition is consistent with the Copenhagen interpretation and in agreement with all measurements performed with detectors at rest in an arbitrary Lorentz (laboratory) frame. From the introduced collapse model follows that under certain conditions multiple measurements are allowed on the same uncollapsed quantum state. An application of the developed approach is shown on measurement of photon-pair state entangled in polarization and energy. Conditions under which two measurements can be taken on the uncollapsed photon-pair state are derived. Serious consequences follow from the allowance of multiple measurements on the same uncollapsed state. For example, the measurements taken by both detectors in this situation are uncorrelated. Moreover, all the conservation laws could be violated in individual measurements, but not in mean values. This statement is proved on the two-photon state entangled in energy. This is in contradiction with experimental results observed by the detectors in rest relative to each other. It is shown that the property of measuring uncorrelated results with detectors in relative movement is related solely to the proposed collapse model. The remaining collapse models---the preferred Lorentz frame, Aharonov-Albert, and Hellwig-Kraus---are examined and discussed with respect to the designed experiment, which involves spacelike separated measurements.

DOI
10.1103/physreva.108.023709

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The relativity of simultaneity together with the definition of a quantum state collapse results in experimental situations where multiple measurements can be taken on an uncollapsed quantum state. The quantum state's collapse is defined to be instantaneous in a rest inertial frame of a detector performing measurements on the quantum system. The definition is consistent with the Copenhagen interpretation and in agreement with all measurements performed with detectors at rest in an arbitrary Lorentz (laboratory) frame. From the introduced collapse model follows that under certain conditions multiple measurements are allowed on the same uncollapsed quantum state. An application of the developed approach is shown on measurement of photon-pair state entangled in polarization and energy. Conditions under which two measurements can be taken on the uncollapsed photon-pair state are derived. Serious consequences follow from the allowance of multiple measurements on the same uncollapsed state. For example, the measurements taken by both detectors in this situation are uncorrelated. Moreover, all the conservation laws could be violated in individual measurements, but not in mean values. This statement is proved on the two-photon state entangled in energy. This is in contradiction with experimental results observed by the detectors in rest relative to each other. It is shown that the property of measuring uncorrelated results with detectors in relative movement is related solely to the proposed collapse model. The remaining collapse models---the preferred Lorentz frame, Aharonov-Albert, and Hellwig-Kraus---are examined and discussed with respect to the designed experiment, which involves spacelike separated measurements.
The nonlocal action of a measurement performed on a quantum entangled particle can determine the quantum state of a distant entangled particle instantly. Since the relativistic simultaneity of events is frame dependent therefore, a physically valid question arises, does the nonlocal action at a distance determine the quantum state of the distant particle in its past, when quantum state collapse is observed from a different inertial frame of reference? From the relativity of simultaneity, Lorentz invariance of the quantum entangled state of photons under consideration and the validity of Bell's theorem in all inertial frames of reference, it is demonstrated that the measurement-induced collapse of a quantum entangled state also determines the quantum state of a distant photon in its past, provided one of the photons is located in the future. The past and future are defined with respect to the time of quantum state collapse in the rest frame of a quantum state measurement device.
A thought experiment is presented that provides a hint as to how quantum wave functions can collapse in a relativistically consistent way. The thought experiment consists of a central source of photon pulses midway between two detectors, which is examined relativistically from both the lab frame and a frame moving with respect to the source and detectors. The total number of pulses between the two detectors is the only invariant and this leads to the idea that collapse might occur along special spacetime intervals, which we call symmetric spacetime intervals. In the current formalism of quantum mechanics, collapse is envisioned to occur “instantaneously”, in clear violation of relativity. It is shown that what the current formalism actually specifies is that collapse is merely spacelike. However, if quantum collapse occurs along symmetric spacetime intervals, then collapse of the wave function can be made consistent with relativity and all observers can agree upon which of two spacelike-separated causally connected events is the cause and which the effect. Nomenclature x = normalized distance in light seconds (ls) t = normalized time in seconds (s) γ = Lorentz factor s = spacetime interval u = normalized velocity (ls/s) c = speed of light (1.0 ls/s) y = a quantum object z = a quantum object d = separation between pulses (ls) L = separation between detectors (ls) ν = frequency (s-1) n = number of pulses β = slope of the symmetric interval (s/ls) I.
This paper aims to clarify the true physical relation of photon pairs and to falsify the "entanglement collapse" hypothesis that standard quantum mechanics imposes upon them. Bell experiments violating Bell's inequality only rule out "local independent hidden variables," and are not a sufficient condition for proving "superposition plus wave-function collapse." The physical definition of entanglement in standard quantum mechanics is: subsystems are strongly correlated, the system is inseparable, and the individual subsystem has no definite independent physical state; its mathematical expressions are the non-factorizability of pure-state wave functions and the non-convex-combination of mixed-state density matrices. The physical definition and mathematical expressions are fully aligned: the individual subsystem cannot be written as a separate expression and has no definite independent physical state. Operationally, it is also absolutely impossible to realize an individual measurement of the subsystem. However, in Bell experiments, photon pairs are separately and individually measured on spatially separated detectors, which directly falsifies the premise that "the photon pair is in an entangled state." Stripping away mysticism, the true relation of two photons is a linear equation with two unknowns (independent particles under an initial-state constraint); the three-photon logic (a linear equation with three unknowns) proves that after measuring one photon, the other two still have not collapsed into definite values and must still be measured individually to obtain their states—"wave-function collapse into a definite value" is purely fictitious in algebraic logic.
Abstract A thought experiment is considered on the observation of the instantaneous collapse of an extended wave packet. According to the relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. The probabilistic nature of quantum-mechanical phenomena eliminates any contradictions between these two apparently conflicting statements. It is shown that the consistency of quantum collapse with relativity follows directly from the Born postulate without any use of mathematical properties of quantum operators, which allows us to discuss this topic in an introductory course of modern physics. The consistency of quantum mechanics with relativity is also shown for instant disentanglement of an extended composite system.
Two of the most common interpretations of quantum measurement disagree about the fate of quantum amplitudes after measurement, yet this disagreement has not previously led to experimentally distinguishable predictions. In the standard collapse picture, commonly linked to the Copenhagen interpretation of quantum mechanics, measurements eliminate unrealized amplitudes without leaving a memory. In contrast, in the unitary theory, the measurement device registers one of the possible outcomes while remaining part of an entangled state that continues to harbor the unrealized amplitudes. This persistence arises naturally under unitary evolution, since a measurement device that is part of an entangled system cannot serve as a faithful probe of the joint quantum state. Using single-photon measurements of a tunable quantum state, we experimentally show that these two theories make different predictions when three or more consecutive measurements are performed on the same quantum system. Analysis of the joint density matrix of the three measurements reveals coherence among them and supports the unitary theory of quantum measurement. When decoherence is explicitly introduced, the joint density matrix of the quantum system of interest and the apparatus becomes consistent with what a collapse theory would predict. This work clarifies the dynamics of consecutive quantum measurements and offers new insights into the interpretation of quantum measurements.
An experimental test of relativistic wave-packet collapse is presented. The tested model assumes that the collapse takes place in the reference frame determined by the massive measuring detectors. Entangled photons are measured at 10 km distance within a time interval of less than 5 ps. The two apparatuses are in relative motion so that both detectors, each in its own inertial reference frame, are first to perform the measurement. The data always reproduces the quantum correlations and thus rule out a class of collapse models. The results also set a lower bound on the `speed of quantum information' to 2/3 ×10 7 and 3/2 ×10 4 times the speed of light in the Geneva and the background radiation reference frames, respectively. The very difficult and deep question of where the collapse takes place—if it takes place at all—is considered in a concrete experimental context.