# Could the collapse of a wave function be used to determine whether an object has been detected?

Consider a ship in space that is attempting to stealthily travel between two locations. I hypothesize that it could use the collapse of a wavefunction to tell if it's been detected by using a particle like an electron that would begin in a superposed state and be exposed to the space outside. If it collapsed to any classical state, the electron would then interact with the ship--for example, by traveling through a circuit--to trigger an alarm.

Could the collapse of a quantum state serve as a useful means of determining whether the ship has been detected in transit? I would expect that in space--especially between two distant galaxies--the probability of an object being observed in the quantum sense due to natural processes to be relatively low given the low matter density. Provided that detection by intelligent life or other automata is possible, is there a way for such a system to use the wave function collapse to determine whether it has indeed been detected?

• Quantum key distribution ( en.wikipedia.org/wiki/Quantum_key_distribution )might be in the spirit of what you're looking for. May 24, 2017 at 5:36
• @WillO Could these principles still apply given the constraints discussed in Mark's answer and comment? It seems like there would still be interaction with a "large system" causing it to collapse irrespective of interaction with the environment.
– user157063
May 26, 2017 at 21:58
• @CAPSLOCK Actually, the No-Cloning Theorem actually helps here. The entangled particles can encode keys for future encrypted communication. If someone tries to intercept the particles to copy the key, they can't do it without being noticed. Either the intended recipient never gets the key, or the key is garbled due to wavefunction collapse. May 27, 2017 at 2:26

To make this device specific, let's say we have an electron in a box and that electron is in a superposition state of being in the right and left side of the box. If there is outside interference or detection, the electron will collapse into a pure left or pure right state.

Here's the problem: how do we check if the electron's wavefunction has collapsed? We have to open the box and look at it. This also counts as a detection, meaning the act of checking the electron's state will result in the collapse of the wavefunction to pure right or pure left. In other words, we can't tell if the electron's wavefunction was already collapsed before we opened the box, or if we collapsed it with the act of opening the box.

In any quantum measurement, we never see a superposition state. We always observe that a particle to be in one and only one of its allowed states. Physicists infer the wavefunction of a particle by making many measurements of identically prepared particles and working backwards from the frequency of observed states to the wavefunction.

Perhaps we might be able to work around this. Imagine that we had a device that could exactly clone the state of the electron in the box without collapsing it. Then, when we wanted to check if we've been detected, we make 1000 clones of the particle and measure those clones. If half of them are pure right and half pure left, then the original particle must be in a superposition state. We're safe for now. If all of the clones are in the same collapsed state (all left or all right), then the original particle must have already collapsed, and we conclude that we've been detected. Battle stations!

Unfortunately, quantum mechanics doesn't allow this. The No-Cloning Theorem, which is derived from the laws of quantum mechanics, states that it is impossible to clone a particle in this way.

• As an alternative to looking in the box, what if there are conductors on the left and right side of the box that are both fed as inputs into a form of Boolean XOR gate? Can we say the state has collapsed iff that gate has a high output? In this case we cannot infer whether left is true or right is true given (left XOR right) is true. Does the state collapse anyway either by us observing the output of the XOR gate or by the XOR gate taking input from the box?
– user157063
May 24, 2017 at 14:41
• @CAPSLOCK That won't work either. If a quantum particle interacts with a large system (large meaning it's made of a large number of particles) in a way that changes the state of the large system (like a measurement), then the wavefunction of the particle collapses in a process called decoherence. en.wikipedia.org/wiki/Quantum_decoherence May 24, 2017 at 19:56