How can you measure the polarization of a single-photon without destroying it?

Question

In Quantum Key Distribution, namely the BB84 protocol, Alice creates single-photons in the horizontal/vertical basis or the (45 degree rotated) diagonal basis which she then sends to Bob over a transmission line.

Now if an eavesdropper Eve that has the ability to measure the polarization of the photons is intercepting this transmission line, she can try to figure out the secret key that Alice is trying to send to Bob. But how can Eve measure the polarization of a single-photon without destroying it?

In videos like this https://youtu.be/uiiaAJ3c6dM?t=171 it looks like the polarization filters are able to measure the polarization of the photons without destroying them. But is that feasible in the real world? I mean if I use a vertical polarization filter to measure a horizontally polarized photon, that photon will be absorbed/destroyed by my filter.

Answer 1

In general, if you want to know the polarization of light experimentally, you need to make a series of measurements in different bases/directions using a different filter each time. Each measurement indeed will destroy a single photon, so in order to fully know the polarization of light you need to measure an ensemble/collection of photons. I think that this is what the linked video is trying to explain: Eve has to choose one basis in which to measure the single photon (and then create a new photon of the measured polarization to send to Bob). However, if Eve chose the wrong basis in which to measure the photon's polarization, she will send Bob a photon of the wrong polarization. The video describes, however, that Alice can send a classical message to Bob to tell him which basis to measure the photon's polarization in.

Answer 2

Eve could use a polarising beam splitter (PBS) crystal instead of a regular polarising filter. The PBS does not destroy the photon, it simply directs vertical photons one way and horizontal photons a different way. Eve could potentially recombine paths and send the photons on to Bob, no matter which way they were initially polarised. The problem arises when Eve tries to determine which path the photon took, after passing through the PBS in order to determine its polarisation. Any attempt by Eve to demine the "which way" information will alter the photons properties in a way that can potentially be detected by Bob. so he could in principle determine that eavesdropping has taken place. For example, Eve could bounce the photon off a tiny mirror. Since photons have momentum, Eve could in principle detect the tiny recoil of the mirror as the photon bounces off it. However, this movement due to the recoil of the mirror will change the phase of the photon and if Alice was sending entangled photons via two paths to Bob, the change in phase will destroy the interference pattern seen by Bob and he will know know something dodgy is going on.

But how can Eve measure the polarization of a single-photon without destroying it?

While eve can potentially measure the polarisation of a single photon without destroying it, any attempt to measure the polarisation will alter the polarisation to a certain extent, whether a PBS or a regular polarising filter is used and this is potentially detectable at the receiving end.

Alternatively Eve could direct the photons exiting the PBS to two detectors, so she will know the polarisation of the photon sent by Alice, but at the cost of destroying the photon with 100% certainty. Let's say she detects a photon on the vertical path. She could then create a vertically polarised photon to continue the journey in place of the destroyed photon. Unfortunately for Eve this attempt to eavesdrop undetected is not perfect, because she cannot create a exact copy of the photon she destroyed because of the "no cloning" theorem of QM and there would be a noticeable delay in the travel time of the photon.