Simulation of non-Hermitian quantum mechanics

In summary, the conversation revolves around a recent research paper published in Communications Physics regarding the simulation of non-Hermitian quantum mechanics using a quantum computer. The paper has been met with skepticism and questions from a freelance researcher who is not well-versed in advanced quantum mechanics. The paper explores open systems and the violation of entanglement monotonicity in postselected subspaces. The findings of the experiment do not enable superluminal communication and the no-go theorems of quantum mechanics still apply in the non-post-selected dynamics.
  • #1
James Essig
TL;DR Summary
I have some questions on recently reported simulations of non-Hermitian quantum mechanics using a quantum computer goes beyond centuries old conventions.
I noticed the research on NHQM in the following news release.
New physics rules tested on quantum computer
Published: 19.2.2021

Information for relevant paper is provided as follows.

Quantum simulation of parity–time symmetry breaking with a superconducting quantum processor

Communications Physics volume 4, Article number: 26 (2021)

Simulation of non-Hermitian quantum mechanics using a quantum computer goes beyond centuries old conventions.

I had two questions regarding this research.

Do the findings of this experiment enable superluminal communication or is a classical signal still required communicate the state of the first qubit to the observer of the second qubit?

Do the no-go theorems of quantum mechanics apply in the NHQM systems studied in the subject experiment?

Note that I am a free-lance researcher working on concepts for relativistic space travel and my field involves classical physics more than quantum mechanics. I have taken two quantum physics courses at the local university I obtained my Bachelor Of Science Degree in Physics but am not well versed in latest research in quantum mechanics.

I would be extremely grateful if you could provide a response to my questions.

Most Respectfully,

James M Essig
BS Physics
George Mason University
Fairfax Virginia, USA.
Physics news on
  • #2
1st of April?
  • #3
Could be the joke was on me. Thanks for your reply to my questions.
  • #4
Still cannot tell is the above paper and report is a practical joke or what. The paper has a lot of what it appears to be formalism that makes extravagant claims. Not being well verse in advanced quantum mechanics, I do not know what to say. It almost sounds too good to be true. If anyone can check out the paper and tell me what they think, I would appreciate that. It could very well be that the paper was a prank.

Thanks, Jim.
  • #5
It looks like a serious publication in Communications Physics. I'm not an expert in this field. So I cannot so easily judge it from just glancing over it though.
  • #6
James Essig said:
Still cannot tell is the above paper and report is a practical joke or what. The paper has a lot of what it appears to be formalism that makes extravagant claims.

The paper is legit, but it does not really make extravagant claims. They even clearly say that these violations of entanglement monotonicity are apparent only. They also clearly state that
"The unitary ##U_{a,q,q′}##, which induces a local non-Hermitian drive of qubit ##q## in the post-selected subspace of the ancilla, is in fact a nonlocal operation on the system qubit ##q## and the ancilla ##a##."

This paper is about open systems - systems interacting with an external environment or bath.
One has three qubits. One may now investigate the full system. For the full system, the authors say (in the supplement, note 3):

"However, in the complete eight dimensional space of system qubits and ancilla, these three-qubits undergo a unitary dynamics and entanglement does not vary under local operations."

In the main paper, they also say:
"The violation of entanglement monotonicity occurs in one postselected subspace."

In a very rough, loose and simplified description, what these guys say is: If you have a system of three entangled qubits, declare two of them as your system of interest and the third as some external environment you ignore or do not know, this partial system consisting of the two qubits may look as if local operations may create entanglement - which, however, is only a consequence of not looking at the full system. The full system behaves as expected and the "local" operation is not really local as explained above by the authors.
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  • #7
If you look at figure 3, you can see where the "magic" is. They're discarding runs where the ancilla qubit is true, and analyzing the leftover data as if they weren't doing that. The result is postselected dynamics that aren't unitary.

Note that e.g. P_111 is not present in the readout column:


> Do the findings of this experiment enable superluminal communication [...]?

No. When you actually run the experiment there is a "keep or discard" signal that has to eventually propagate to all qubits (or to all measurement results from those qubits).

> Do the no-go theorems of quantum mechanics apply in the NHQM systems studied in the subject experiment?

If you're talking about the postselected dynamics implied by interpreting the kept data as if it was all the data, then some apply and some don't. For example, no-cloning will still hold but no-signalling won't. That being said, I want to re-emphasize that the theorems still hold when you consider all of the data and that you need to be very careful not to confuse yourself by mixing up the post-selected dynamics with the non-post-selected dynamics.

Related to Simulation of non-Hermitian quantum mechanics

1. What is non-Hermitian quantum mechanics?

Non-Hermitian quantum mechanics is a theoretical framework that extends traditional Hermitian quantum mechanics to include systems that violate the Hermitian symmetry condition. This condition states that the Hamiltonian operator must be equal to its adjoint, or Hermitian conjugate. Non-Hermitian systems can exhibit unique properties such as non-reciprocal behavior and non-unitary time evolution.

2. How is non-Hermitian quantum mechanics simulated?

Non-Hermitian quantum mechanics can be simulated using a variety of numerical and analytical methods. These include the finite-difference time-domain method, the scattering matrix method, and the non-Hermitian spectral method. Each method has its own advantages and limitations, and the choice of method depends on the specific system being studied.

3. What are some applications of simulating non-Hermitian quantum mechanics?

Simulating non-Hermitian quantum mechanics has many potential applications in fields such as photonics, quantum computing, and quantum information processing. It can also be used to study complex systems with non-Hermitian interactions, such as open quantum systems and dissipative systems.

4. What are some challenges in simulating non-Hermitian quantum mechanics?

One of the main challenges in simulating non-Hermitian quantum mechanics is the presence of non-orthogonal eigenstates, which can lead to non-Hermitian operators having complex eigenvalues. This can make numerical simulations more difficult and require the use of specialized algorithms. Additionally, the interpretation of results from non-Hermitian systems can be more complex and may require new theoretical frameworks.

5. How does non-Hermitian quantum mechanics relate to other branches of physics?

Non-Hermitian quantum mechanics has connections to other branches of physics, such as classical mechanics and statistical mechanics. It also has implications for the study of symmetry breaking and phase transitions in quantum systems. Additionally, non-Hermitian systems have been studied in the context of non-relativistic quantum field theory and quantum gravity.

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