Effect of acceleration on entanglement

[Dragonfall]

If two parties share some entangled state, one party accelerates. Does that affect the joint state?

This is coming from quantum information theory's point of view. I remember there were some pure states that becomes mixed states under acceleration (or vice versa). I wonder what happens if half of a pure entangled state goes under acceleration.

 

[bhobba]

If two parties share some entangled state, one party accelerates. Does that affect the joint state?

To the best of my knowledge it makes no difference.

Thanks
Bill

 

[Nugatory]

I remember there were some pure states that becomes mixed states under acceleration (or vice versa).

Do you have have a reference?

 

[Dragonfall]

Do you have have a reference?

I can't find the exact reference. I can only piece together from Wikipedia something called the "Unruh effect" which says that an accelerating observer sees block-body radiation whereas inertial ones don't. Then (a miracle occurs and) the thermal state of vacuum is pure for inertial observer but mixed for an accelerating one.

 

[mfb]

Entangled in what, accelerated how?
The experiment matters.

Usual accelerations lead to negligible Unruh radiation.

 

[Dragonfall]

Two spin-entangled electrons in magic boxes. One of them accelerates by an amount that will make this thought experiment interesting.

 

[atyy]

I can't find the exact reference. I can only piece together from Wikipedia something called the "Unruh effect" which says that an accelerating observer sees block-body radiation whereas inertial ones don't. Then (a miracle occurs and) the thermal state of vacuum is pure for inertial observer but mixed for an accelerating one.

One key idea is the reduced density matrix. The reduced density matrix is also how decoherence produces a mixed state from a pure state. The pure state must be an entangled state (in some sense). However, for an accelerated observer there is more physics going on that just that the reduced density is mixed. Even if Alice and Bob are both moving with constant velocity in an inertial frame, if they share an entangled pair, Bob's state will be mixed.

Eg. http://arxiv.org/abs/1109.1283 "It has been known for some time, motivated by studies of Unruh radiation and Hawking radiation, that the spectrum of the reduced density matrix of a half space in a relativistic quantum field theory is related to that of the Lorentz boost generator that preserves the so-called Rindler wedge"

See also: http://web.stanford.edu/~phayden/bellairs2007/alsing_slides2.pdf which has a great summary.
-For bosonic scalar field, the entanglement degrades with increasing acceleration
-For fermionic Dirac field, the entanglement saturates with increasing acceleration

However, the detection of the Unruh radiation is not dependent on trans-horizon entanglement. See http://arxiv.org/abs/1108.0320 and Demystifier's post in https://www.physicsforums.com/threads/unruh-shadow.820185/.

 

[Dragonfall]

OK that physics is very much over my head, but thanks a bunch.

My motivation was that introducing entanglement into multi-party computation (even with purely classical communication) results in all kinds of headaches. If there were a way to just "take a party and shake him" until any entanglement he shared with anyone else becomes too degraded to use, it would have made things much simpler.

 

[atyy]

OK that physics is very much over my head, but thanks a bunch.

My motivation was that introducing entanglement into multi-party computation (even with purely classical communication) results in all kinds of headaches. If there were a way to just "take a party and shake him" until any entanglement he shared with anyone else becomes too degraded to use, it would have made things much simpler.

Yes, things are more complicated than that BUT I do think your intuition is good - but I am not sure, it would be interesting to discuss this point. The intuition is this: the maximal entanglement of a Bell pair is pretty delicate, and the experiment requires a special setup, which is why one doesn't see a Bell inequality violation every day. If the maximal entanglement is delicate, presumably heating the apparatus which is random jiggling should destroy the maximal entanglement. The Unruh radiation is a form of heating and should destroy the entanglement.

Another way to say it is that is the pair interacts with many other particles, the entanglement should get diluted because of monogamy of entanglement.

But it is surprising to me that the effect is not quite the same with fermions and bosons - so I would love to see more discussion on the relationship between the intuition and the correct calculation!

 

[Nugatory]

My motivation was that introducing entanglement into multi-party computation (even with purely classical communication) results in all kinds of headaches.

How so? You cannot even determine whether entanglement was present or not until you've brought all the observers together so that they can compare notes after they've completed and recorded their observations.

 

[Dragonfall]

How so? You cannot even determine whether entanglement was present or not until you've brought all the observers together so that they can compare notes after they've completed and recorded their observations.

Usually you assume that some subset of the parties have shared entanglement a priori.

 

[Dragonfall]

Yes, things are more complicated than that BUT I do think your intuition is good - but I am not sure, it would be interesting to discuss this point. The intuition is this: the maximal entanglement of a Bell pair is pretty delicate, and the experiment requires a special setup, which is why one doesn't see a Bell inequality violation every day. If the maximal entanglement is delicate, presumably heating the apparatus which is random jiggling should destroy the maximal entanglement. The Unruh radiation is a form of heating and should destroy the entanglement.

Another way to say it is that is the pair interacts with many other particles, the entanglement should get diluted because of monogamy of entanglement.

But it is surprising to me that the effect is not quite the same with fermions and bosons - so I would love to see more discussion on the relationship between the intuition and the correct calculation!

I am in the wrong field to say anything meaningful, unfortunately. But entanglement distillation protocols only need classical communication. So our intuition must destroy entanglement faster than they can repair, in a sense. If they have classical communication.

 

[DrChinese]

If two parties share some entangled state, one party accelerates. Does that affect the joint state? ...

Two spin-entangled electrons in magic boxes. One of them accelerates by an amount that will make this thought experiment interesting.

The first thing I think of, is: HOW are you going to accelerate an entangled system? That will require application of a force to a quantum system. By definition that requires an interaction. That is hardly trivial to answering your question.

If you are accelerating via gravity, the effect is negligible because Bell tests are performed in the Earth's gravitational field all the time. There is no known effect due to gravity.

But some types of force application might well amount to a measurement. Then the entanglement would not continue.

 

[atyy]

To add to the thoughts in post #9, there are pretty good references in http://arxiv.org/abs/1006.1394v3 "Unveiling quantum entanglement degradation near a Schwarzschild black hole" by E. Martin-Martinez, L.J. Garay, J. Leon.

DuckDuckGo ("unruh AND entanglement AND degradation") suggests:

http://arxiv.org/abs/1503.07526
http://dx.doi.org/10.1103/PhysRevA.92.022334
Degradation of entanglement between two accelerated parties: Bell states under the Unruh effect
Benedikt Richter, Yasser Omar
We study the entanglement of families of Unruh modes in the Bell states |Φ±⟩=1/2√(|00⟩±|11⟩) and |Ψ±⟩=1/2√(|01⟩±|10⟩) shared by two accelerated observers, and find fundamental differences in the robustness of entanglement against acceleration for these states. States Ψ± are entangled for all finite accelerations, whereas, due to the Unruh effect, states Φ± lose their entanglement for finite accelerations. This is true for Bell states of two bosonic modes, as well as for Bell states of a bosonic and a fermionic mode. But also for Bell states of fermionic modes there are differences in the degradation of entanglement. We reveal the origin of these distinct characteristics of entanglement degradation and discuss the role that is played by particle statistics. Our studies suggest that the behavior of entanglement in accelerated frames strongly depends on the occupation patterns of the constituent states, whose superposition constitutes the entangled state, where especially states Φ± and Ψ± exhibit distinct characteristics regarding entanglement degradation. Finally, we point out possible implications of hovering over a black hole for these states.

 

[Strilanc]

If there were a way to just "take a party and shake him" until any entanglement he shared with anyone else becomes too degraded to use, it would have made things much simpler.

That plan will backfire horribly. If any of a set of qubits in a GHZ state like $\frac{1}{\sqrt{2}} \left|000\right\rangle + \frac{1}{\sqrt{2}} \left|111\right\rangle$ decoheres or gets measured, the whole state will collapse and you will lose any quantum benefits.

The only way to remove a qubit from a GHZ state is to get it and another involved qubit in one place and make them interact (e.g. you can toggle one of them with a CNOT controlled by the other). The same is true of other entangled states, except sometimes you'll need more than two of the involved qubits.

 

[Physics Monkey]

I think the effects of acceleration on entanglement depend on the physical manifestation of the logical state.

For example, http://arxiv.org/abs/1006.1394v3 considers entangled states made of modes of scalar and spinor fields. Since these modes transform non-trivially under accelerations it is conceivable that acceleration can affect the entanglement in this case (as these and other authors show).

On the other hand, if two observers share an entangled pair of qubits instantiated, say, as superconducting qubits inside refrigerators, then I don't think there is any universal affect due to accelerating one superconducting qubit relative to another. The interaction necessary to accelerate the system or Unruh radiation may eventually decohere the entanglement, but I don't think the acceleration itself has an effect.

An interesting question is photons. Since we envision beaming quantum information all over the place using photons as carriers, perhaps there is some room for an interesting acceleration effect here. My intuition is that such an affect would be small and could be dealt with using quantum error correction, but I'm not familiar with the literature on this topic.

 

[Dragonfall]

That plan will backfire horribly. If any of a set of qubits in a GHZ state like $\frac{1}{\sqrt{2}} \left|000\right\rangle + \frac{1}{\sqrt{2}} \left|111\right\rangle$ decoheres or gets measured, the whole state will collapse and you will lose any quantum benefits.

That's kind of the point. There are two parties I don't trust. Somehow, I am able to prevent them from communicating for the duration of some protocol. But they may still have shared entanglement. I want their shared state to collapse so that they can't adopt any entanglement-assisted strategy.

 

[Strilanc]

That's kind of the point. There are two parties I don't trust. Somehow, I am able to prevent them from communicating for the duration of some protocol. But they may still have shared entanglement. I want their shared state to collapse so that they can't adopt any entanglement-assisted strategy.

Nothing you do on your own locally can affect whether or not they can coordinate with each other or their expected measurements. If that wasn't the case, you could use it for FTL communication.

For example, the fact that you have one of the pieces of the GHZ state already acts like a measurement from their perspective; it's just that it can be undone with your help.

 

[Dragonfall]

Nothing you do on your own locally can affect whether or not they can coordinate with each other or their expected measurements. If that wasn't the case, you could use it for FTL communication.

For example, the fact that you have one of the pieces of the GHZ state already acts like a measurement from their perspective; it's just that it can be undone with your help.

Think of the other parties in small, literal black-boxes in your possession. Ones that you can take up and literally shake.