# Weak quantum measurement, or Resuscitation for a Schrodinger cat

Today, wandering around the Internet, I came across a description of an experiment by a group of American scientists led by Nadav Katz, who were able to reverse the collapse of the qubit wave function, thereby confirming the theory of Alexander Korotkov and Andrew Jordan.

So far, the scientific community has been very wary of this result; however, if the Korotkov-Jordan theory is correct (and it seems to be true), then this will lead to a revolution, first in quantum mechanics, then in modern physics, and then simply turn the world upside down. Exactly.

Now I’ll try to explain why.

I think we all know the thought experiment with the Schrodinger cat well. Let me remind you, just in case: a cat is placed in a closed box, an ampoule with poison and an unstable core, which will decay in the next hour with a probability of 50%. In this case, if the nucleus disintegrates, the ampoule with the poison will open and the cat will die.

From the point of view of quantum mechanics (more precisely, the Copenhagen interpretation of quantum mechanics), until we open the lid and check the state of the cat, he will be in a superposition of both states - both alive and dead at the same time. At the moment of measuring the state of the cat, the so-called collapse of the wave function - the system will choose one of two possible states, and the cat will either live on or die forever.

In general, any quantum system is in a superposition of all its possible states until a measurement takes place and it accepts one of the possible states.

And so, in 2006, Korotkov and Jordan published an article entitled "Uncollapsing the wave function by undoing quantum measurements" , which can roughly be translated into Russian as "Canceling the collapse of the wave function by canceling the quantum measurement."

Its meaning is as follows: well, a direct measurement of the state of the system will lead to the collapse of the wave function and the choice of one of the states. But, let's say that we can measure the state of the system not directly, but with the help of the so-called weak measurement ( weak measurment) - such a measurement in which the measuring device interacts weakly with the measured object and complete collapse of the wave function does not occur. Then, according to Korotkov and Jordan, we can not only measure the state indirectly, but also do it several times; Moreover, if the result of the experiment does not suit us, we can return the system back and try again.

If we apply the Korotkov-Jordan theory to the Schrödinger cat, it will look something like this: we can not open the box, but slightly open it and look with one eye; if we see that the cat is dead, we can close the box, wait a while, look again and see the cat alive!

It sounds crazy and fantastic, but in 2008, Nadav Katz and his group managed to conduct an experiment.in which she actually performed a similar sequence of actions.

The Katz group placed the qubit in a state of superposition from both of its states - high and low energy. Any attempt to directly measure the energy of a qubit would lead to the collapse of the wave function and the transition of the qubit to one of two states.

Further, the following happened: with the help of a weak measurement of magnetic fields, the Katz team received information about the state of the qubit (0 or 1). In this case, the qubit partially collapsed in the direction of the measured state. If this state turned out to be zero, the Korotkov-Jordan procedure of “canceling the collapse” was carried out: the qubit received a magnetic impulse, which translated it into a strictly opposite state, after which the exact same weak measurement of its state was made. The result of these three operations (weak measurement of state 1 - reverse - weak measurement of state 2) was the transfer of the qubit into exactly the same state of uncertainty in which it was before all these manipulations (i.e., two measurements actually cancel each other's influence). In other words, scientists measured the state of the "cat", and if he was dead,

Here is a detailed description of the experiment, if someone does not believe: the original , the article is in Russian .

Now let's talk about what consequences this could potentially lead to.

In 1935, Einstein, with a group of like-minded people, trying to challenge the Copenhagen interpretation of quantum mechanics, formulated a paradox, later called the Einstein-Podolsky-Rosen paradox (ERP paradox).

The Heisenberg uncertainty relation states that both the position and momentum of a quantum system cannot be measured absolutely accurately. Well, Einstein said, and if we take a system of two identical particles, and measure the momentum of one of them, and the position of the other, do we violate the uncertainty principle?

As it turned out, no. Measurement of the state of one of the "entangled" particles led to the collapse of the state of the other particle, no matter how far they are from each other. This phenomenon has been repeatedly confirmed experimentally - in the strongest experiment, the particles were at a distance of 144 kilometers from each other.

Thanks to quantum confusion, the so-called quantum cryptography. Let's say Anna and Boris have a box of entangled photons. They leave for different countries, each taking half of the photons with them. Next, Anna measures the state of the first photon. His pair in Boris's box automatically assumes the same state. T.O. You can generate an encryption key that only Anna and Boris will know at the same time. Further, the message is encrypted with this key and forwarded.

Although the collapse of entangled particles occurs instantly, the transfer of information, as was thought until recently, is thus impossible, because Anna does not have the ability to influence the choice of state with her photon. But Korotkov and Jordan suggested, and the Katz group experimentally verified that there was such an opportunity!

If Anna and Boris had a box of confused qubits, then Anna, using the procedure for canceling the collapse of the wave function, could “get” the first qubit out of the box as many times as she needed, until he finally assumes the exact state that Anna needs. At the same time, Boris’s qubit will assume exactly the same state - it turns out that Anna sends information to Boris INSTANTLY.

But instant transmission of information is only the tip of the iceberg. According to the meaning of the Korotkov-Jordan theory, we can cancel the results of any experiment (so far, however, with the “quantum” clause), if it does not suit us, and try again - in general, any number of times until we get an acceptable result.

In fact, if the reasoning described above can actually be reproduced, then we are somewhere on the verge of absolutely incredible changes in physics, which will then change our whole life beyond recognition.

So far, the scientific community has been very wary of this result; however, if the Korotkov-Jordan theory is correct (and it seems to be true), then this will lead to a revolution, first in quantum mechanics, then in modern physics, and then simply turn the world upside down. Exactly.

Now I’ll try to explain why.

I think we all know the thought experiment with the Schrodinger cat well. Let me remind you, just in case: a cat is placed in a closed box, an ampoule with poison and an unstable core, which will decay in the next hour with a probability of 50%. In this case, if the nucleus disintegrates, the ampoule with the poison will open and the cat will die.

From the point of view of quantum mechanics (more precisely, the Copenhagen interpretation of quantum mechanics), until we open the lid and check the state of the cat, he will be in a superposition of both states - both alive and dead at the same time. At the moment of measuring the state of the cat, the so-called collapse of the wave function - the system will choose one of two possible states, and the cat will either live on or die forever.

In general, any quantum system is in a superposition of all its possible states until a measurement takes place and it accepts one of the possible states.

And so, in 2006, Korotkov and Jordan published an article entitled "Uncollapsing the wave function by undoing quantum measurements" , which can roughly be translated into Russian as "Canceling the collapse of the wave function by canceling the quantum measurement."

Its meaning is as follows: well, a direct measurement of the state of the system will lead to the collapse of the wave function and the choice of one of the states. But, let's say that we can measure the state of the system not directly, but with the help of the so-called weak measurement ( weak measurment) - such a measurement in which the measuring device interacts weakly with the measured object and complete collapse of the wave function does not occur. Then, according to Korotkov and Jordan, we can not only measure the state indirectly, but also do it several times; Moreover, if the result of the experiment does not suit us, we can return the system back and try again.

If we apply the Korotkov-Jordan theory to the Schrödinger cat, it will look something like this: we can not open the box, but slightly open it and look with one eye; if we see that the cat is dead, we can close the box, wait a while, look again and see the cat alive!

It sounds crazy and fantastic, but in 2008, Nadav Katz and his group managed to conduct an experiment.in which she actually performed a similar sequence of actions.

The Katz group placed the qubit in a state of superposition from both of its states - high and low energy. Any attempt to directly measure the energy of a qubit would lead to the collapse of the wave function and the transition of the qubit to one of two states.

Further, the following happened: with the help of a weak measurement of magnetic fields, the Katz team received information about the state of the qubit (0 or 1). In this case, the qubit partially collapsed in the direction of the measured state. If this state turned out to be zero, the Korotkov-Jordan procedure of “canceling the collapse” was carried out: the qubit received a magnetic impulse, which translated it into a strictly opposite state, after which the exact same weak measurement of its state was made. The result of these three operations (weak measurement of state 1 - reverse - weak measurement of state 2) was the transfer of the qubit into exactly the same state of uncertainty in which it was before all these manipulations (i.e., two measurements actually cancel each other's influence). In other words, scientists measured the state of the "cat", and if he was dead,

Here is a detailed description of the experiment, if someone does not believe: the original , the article is in Russian .

Now let's talk about what consequences this could potentially lead to.

### The Einstein-Podolsky-Rosen Paradox

In 1935, Einstein, with a group of like-minded people, trying to challenge the Copenhagen interpretation of quantum mechanics, formulated a paradox, later called the Einstein-Podolsky-Rosen paradox (ERP paradox).

The Heisenberg uncertainty relation states that both the position and momentum of a quantum system cannot be measured absolutely accurately. Well, Einstein said, and if we take a system of two identical particles, and measure the momentum of one of them, and the position of the other, do we violate the uncertainty principle?

As it turned out, no. Measurement of the state of one of the "entangled" particles led to the collapse of the state of the other particle, no matter how far they are from each other. This phenomenon has been repeatedly confirmed experimentally - in the strongest experiment, the particles were at a distance of 144 kilometers from each other.

Thanks to quantum confusion, the so-called quantum cryptography. Let's say Anna and Boris have a box of entangled photons. They leave for different countries, each taking half of the photons with them. Next, Anna measures the state of the first photon. His pair in Boris's box automatically assumes the same state. T.O. You can generate an encryption key that only Anna and Boris will know at the same time. Further, the message is encrypted with this key and forwarded.

Although the collapse of entangled particles occurs instantly, the transfer of information, as was thought until recently, is thus impossible, because Anna does not have the ability to influence the choice of state with her photon. But Korotkov and Jordan suggested, and the Katz group experimentally verified that there was such an opportunity!

If Anna and Boris had a box of confused qubits, then Anna, using the procedure for canceling the collapse of the wave function, could “get” the first qubit out of the box as many times as she needed, until he finally assumes the exact state that Anna needs. At the same time, Boris’s qubit will assume exactly the same state - it turns out that Anna sends information to Boris INSTANTLY.

But instant transmission of information is only the tip of the iceberg. According to the meaning of the Korotkov-Jordan theory, we can cancel the results of any experiment (so far, however, with the “quantum” clause), if it does not suit us, and try again - in general, any number of times until we get an acceptable result.

In fact, if the reasoning described above can actually be reproduced, then we are somewhere on the verge of absolutely incredible changes in physics, which will then change our whole life beyond recognition.

**UPD**. A number of commentators accuse me of ignorance; I easily admit it, since I have never been a theoretical physicist and wrote everything as I understood. If someone understands the question better than me, I would read with great interest a post with clarification / deeper description of the question.