Honoring Epimenides of Crete \(±Δx\): From Quantum Paradoxes, through Weak Measurements, to the Nature of Time

2.2 IFM 

While the first quantum experiment presents a spatial oddity, later variations of it were 

equally opposed to classical notions of time and causality, hence we introduce it first.  

Consider a super-sensitive bomb with which even the slightest interaction possible leads to 

its explosion. Can one detect the bomb’s presence at a certain location without destroying it? 

Elitzur and Vaidman [16] posed this question with a new answer in the positive. Their 

solution was based on the device known as Mach-Zehnder Interferometer (MZI), shown in 

Fig. 1. A single photon impinges on the first beam splitter, the transmission coefficient of 

which is 50%. The transmitted and reflected parts of the wave-function are then reflected by 

the two solid mirrors and then reunited by a second beam splitter with the same transmission 

coefficient. Two detectors are positioned to detect the photon after it passes through the 

second beam splitter. The positions of the beam splitters and the mirrors are arranged in such 

a way that (due to destructive and constructive interference) the photon is never detected by 

detector D, but always by C. In order to test the bomb, let it be placed on one of the MZI’s 

routes (v) and let a single photon pass through the system. Three outcomes of this trial are 

now possible: 

• The bomb explodes, 

• Detector C clicks, 

• Detector D clicks. 

If detector D clicks (the probability for which being 1/4), the goal is achieved: we know that 

interference has been disturbed, ergo, the bomb is inside the interferometer. Yet, it did not 

explode. 

The problem can be formulated in an even more intriguing way: Can one test whether the 

supersensitive bomb is “good” (better say: “bad”) without bringing about its explosion?

Again, all one should do is to place the bomb on one of the MZI’s routes such that, if the 

photon passes on that route, the bomb’s sensitive part can be triggered by absorbing only 

some of the photon’s energy. Here too, the bomb constitutes a “which way” detector: Just as 

its explosion would indicates that the photon took the bomb’s route, its silence indicates that 

it took the other route. 

Fig. 1. Interaction Free Measurement. BS

1

and BS

2

are beam splitters. In the absence of the 

obstructing bomb, there will be constructive interference at path c (the detector C will click) and 

destructive interference on path d (detector D never clicks). 

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And again, interference is destroyed by the bomb’s mere non-explosion, indicating that the 

bomb is explosive. Since the EV paper, numerous works, experimental and theoretical, have 

elaborated it and expanded its scope. Zeilinger et al. [17] refined it so as to save nearly 100% 

of the bombs. Other applications of IFM range from quantum computation [18] to imaging 

[19]. 

2.3 Partial Measurements - Hybridizing IFM with EPR 

Apart from its technological applications, IFM is extremely efficient for experiments that 

aim to give better understanding of the nature f the wave-function. One such an experiment 

has been proposed [20] for studying the EPR effect. Consider a particle split not only to two 

parts, as in the ordinary MZI, but to 100. Then measure one of the wave-function’s parts. In 

most cases, no detection would occur. This is a weak IFM that changes the wave-function 

only slightly. Rather than the abrupt transition from superposition to position, the likelihood 

of the particle to be in a certain state has increased or decreased. This is partial measurement. 

Next consider an EPR pair whose particles undergo partial measurements. Here, some 

intriguing effects occur: 

1. Partial measurement on one particle yields a partial nonlocal effect on the other particle; 

2. The other particle can then undergo another partial measurement and exert its own slight 

effect back on the first. 

3. Partial measurement can be totally time-reversed, returning the wave-function to its 

original superposition, giving rise to a new kind of quantum erasure. 

4. This erasure nonlocally erases the previous partial nonlocal effect on the distant particle. 

5. This way, the particles may keep “talking” to one another for a long time, unlike the 

ordinary EPR in which they become disentangled after one measurement. This method, and 

the ones describe below, have this feature in common. Quantum measurement is ill-

understood and abrupt. If one makes it gradual, some novel features of the measuring 

process emerge. 

2.4 MAKING IFM MUTUAL: SUPERPOSED PARTICLES MEASURE ONE 

ANOTHER

Next we study more advance variants. To understand their intriguing nature, recall that the 

uniqueness of IFM lies in an exchange of roles: The quantum object, rather than being the 

subject of measurement, becomes the measuring apparatus itself, whereas the macroscopic 

detector is the object to be measured. In their original paper, Elitzur and Vaidman mentioned 

the possibility of an IFM in which both objects, the measuring one as well as the one being 

measured, are single particles, in which case even more intriguing effects can appear. This 

proposition was taken up in a seminal work by Hardy [21]. He considered an EV device 

(Fig. 1) similar to that described in Section 2.1, but with a more delicate “bomb,” henceforth

named a “Hardy atom”. This atom’s state is as follows. Let a spin-1/2 atom be prepared in an 

“up” spin-x state (X

+

) and then split by a non-uniform magnetic field B into its z

components. The two components are carefully put into two boxes Z

+

and Z

−

while keeping 

their superposition state: 

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