The physicist generalized the postulate of measurement in quantum mechanics

PICTURE: A complete measure. If a detector is placed immediately after the three slits. view After

Credit: © Science China Press

The measurement postulate is crucial for quantum mechanics. If we measure a quantum system, we can only get one of the eigenvalues ​​of the measured observable, like position, energy, etc., with a probability. Immediately after the measurement, the system will instantly collapse into the corresponding clean state, called collapse state. It is argued that the non-cloning theorem is in fact the result of the measurement postulate, since the non-cloning theorem would also be valid in classical physics. The possibility of cloning in classical physics is in fact the ability to fully measure a classical system, so that a classical state can be measured and prepared. [1].

To clearly explain the measurement in quantum mechanics, it is better to use the following example. Suppose a photon passes through three identical slits and we place an ideal and non-demolition detector after each of the slits. According to the measurement postulate, one of the detectors will detect the photon and therefore the entire wave function will collapse in that slit.

What will happen if we only place one detector after the top slit? It is natural to think that it will have a one-third probability of detecting the photon and reduce the entire wave function in slit-1, as shown in Figure 2. However, what if the upper slit detector does not measure the photon? This is a partial measure. This was encountered in the formalism of duality quantum computing, where the linear combination of units (LCU) was proposed to perform quantum computing [2].

In Ref. [3], using the LCU formalism [2,4,5], Long proposed that when measuring a partial wave, something will surely happen: (1) collapse: it will collapse into one of the eigenvalues ​​with a certain probability. After the measurement, the whole wave function will instantly change to the corresponding eigenstate; (2) collapse: the measured wave function will disappear and switch to the unmeasured part. As shown in Figure 2, the detector will measure the photon with a probability of 1/3, and the entire wave function of the photon will collapse in the supper slit. As shown in Fig. 3 for the collapse, the part measured in the upper slit disappears and the unmeasured part, namely the wave function in the middle slit and the lower slit, increases.

In reality, partial measurement is more common than full measurement. It should be noted that the collapse and collapse of a partial measure occurs randomly not only in space, but also in time. For example, the detection of photons by a detector is naturally apprehended from this postulate of partial measurement. When the wave function of a photon goes to a detector, it is not fully measured at the same time, i.e. it is not a full measurement. Its front end first arrives at the detector, hitting an area of ​​the detector. It either collapses at any point of the intersection zone in the detector or collapses and the corresponding probability will be shifted to another part of the wave function. This process continues until the photon is detected. If the photon was not detected before the last part of the wave function reaches the detector, then the amplitude of this remaining wave function increases to 1 in order to detect the photon with certainty at the final step.

This explanation is given from the point of view that the wave function is only the entity of the quantum system itself, the WISE interpretation [2,6]. In the WISE interpretation, there is NO relationship between the wave function and the quantum system, the wave function IS just the quantum system. The interpretation of WISE is supported by the experience of delayed choice of encounter [6], which was reported in various media a few years ago [7].


[1] Shen, Y., Hao, L. and Long Gui-Lu. (2011). Why can we copy classic information? Chinese letters of physics, 28 (1), 010306.

[2] Long, Gui-Lu. (2006). General principle of quantum interference and duality computer. Communications in Theoretical Physics, 45 (5), 825.

[3] Long, GL, (2021) Collapse-in and Collapse-out in partial measurement in quantum mechanics and its WISE interpretation, SCIENCE CHINA Physics, Mechanics & Astronomy, https: //do /ten.1007 /s11433-021-1716-y

[4] Long, Gui-Lu. & Liu, Y. (2008). Duality calculus in quantum computers. Communications in Theoretical Physics, 50 (6), 1303.

[5] Long, Gui-Lu, Liu, Y., & Wang, C. (2009). Admissible generalized quantum gates. Communications in Theoretical Physics, 51 (1), 65.

[6] Long, G., Qin, W., Yang, Z. and Li, JL (2018). Realistic interpretation of quantum mechanics and a delayed encounter-choice experiment. SCIENCE CHINA Physics, Mechanics & Astronomy, 61 (3), 030311.

[7] https: // /pub_releases /2018-01 /scp-etr010418.php

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