Help with quantum computing notation

In summary: The first two states, φ+ and φ-, are called symmetric states because they are symmetric under exchange of the two particles, while the last two states, ψ+ and ψ-, are called antisymmetric states. These states are useful for quantum communication and quantum computing protocols. In summary, the conversation discusses the concept of entanglement between photons and how their polarization can be entangled in four different ways. These four states, known as Bell states, are important for quantum communication and computing. The main idea is that entangled photons can have their polarization correlated in different ways, and this can be useful for various applications.
  • #1
Joao
80
8
Hi everyone! Sorry for the bad English!
I'm trying to read the "entanglement between photons that never coexisted " from 2012. Avaliable at: https://arxiv.org/abs/1209.4191

And there's this equation:
##
|φ± \rangle = \frac 1{√2}(|HaHb ± |VaVb\rangle)
##
##
|ψ± \rangle = \frac 1{√2}(|HaVb ± |VaHb\rangle)
##
where ha(vb) represents a horizontally (vertically) polarized photon in spatial mode a (b).

Soooo, I guess what it is saying is:
When photons are entangled, their polarization can be entangled in 4 different ways:
φ+ they have the same "polarization degree" (like vertical and vertical, or horizontal and horizontal) and the same phase (like when one wave is in "Crest" the other will also be in "crest")
φ- they have the same "polarization degree" but opposite phases.
ψ+ they have the opposite "polarization degree" (like horizontal and vertical) and the same phase.
ψ- they have the opposite "polarization degree" and the opposite phase.

And in our BBO cristal we create entangled photons, but we have no clue on what kind of entanglement they have until we measure it.

So far I understood correctly?
Thanks! =)
 
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  • #2
Joao said:
So far I understood correctly?
Yes, that is correct.

For reference, these four basis states are called Bell states and correspond to a two-particle basis in which each state corresponds to an entangled state.
 

1. What is quantum computing notation?

Quantum computing notation is a system of symbols and rules used to represent and manipulate quantum information in a quantum computer. It is similar to traditional computing notation, but it takes into account the unique properties of quantum mechanics.

2. Why is quantum computing notation important?

Quantum computing notation is important because it allows us to accurately describe and analyze the behavior of quantum systems. It also enables us to design and implement algorithms for quantum computers, which have the potential to solve certain problems much faster than classical computers.

3. What are the basic elements of quantum computing notation?

The basic elements of quantum computing notation include qubits (quantum bits), gates (operations that manipulate qubits), and measurements (ways to extract information from qubits). These elements are represented by symbols such as |0⟩, |1⟩, X, Y, Z, and H.

4. How is quantum computing notation different from classical computing notation?

Quantum computing notation is different from classical computing notation in several ways. Firstly, classical computing uses bits, which can only have a value of 0 or 1, while quantum computing uses qubits, which can exist in a superposition of both 0 and 1. Additionally, classical computing uses logic gates such as AND, OR, and NOT, while quantum computing uses gates such as the Hadamard gate and the CNOT gate.

5. Can anyone learn quantum computing notation?

Yes, anyone can learn quantum computing notation with dedication and practice. However, it does require a strong understanding of linear algebra and quantum mechanics. It is recommended to start with the basics and gradually build up knowledge and skills through online resources, courses, and hands-on experience with quantum computing platforms.

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