Can we look upon entanglement as measurement?

In summary, the conversation discusses the interpretation of the state of an entangled photon, specifically in the context of a two-photon entangled state and the reduced density operator obtained by tracing over one photon. It is debated whether this reduced state should be seen as a statistical mixture or a linear superposition. The conversation also references a paper on the topic and provides a link for further discussion.
  • #1
Albert V
26
0
Hi,

I have a question about how to interpret the state of an entangled photon

H = horisontal, V = vertical polarization



The global state is |Phi> = (|H>|V> + |V>|H>)/sqrt2.

By density operator formalism:

rho = |Phi><Phi|
= (1/2) ( |H>|V><H|<V| + |H>|V><V|<H| + |V>|H><H|<V| + |V>|H><V|<H| ).

in order to find the state on the right side, trace out the left side :

rho_right = Tr_left(rho) = (1/2) (|H><H|+|V><V|),

How should this state be interpreted? 1) as a photon EITHER in H OR V, or 2) a mixed state (superposition) containing components of both the left and the right side.

This would help me to understand this paper:

http://arxiv.org/abs/1301.1673
 
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  • #2
First of all, you start with a two-photon state with entangled photons. It's a pure state given by a normalized state ket [itex]|\Phi \rangle[/itex]. The corresponding statistical operator of the pure state is the projection operator [itex]\hat{\rho}_{2 \gamma}=|\Phi \rangle \langle \Phi|[/itex]. This gives you the statistical properties on the polarization of both photons according to Borns rule.

Now you want to forget about the fact that you deal with a two-photon state and only know about the polarization state state of one photon. Thus you trace over the other photon's polarization states to end up with your reduced density operator [itex]\hat{\rho}_{\text{right}}=1/2 \mathbb{1}[/itex]. This shows that an observer only looking at this photon's polarization measures an totally unpolarized beam of photons, i.e., he finds with probability 1/2 either a horizontally or a vertically polarized photon, and that's it.
 
  • #3
Thanks for your answer, but when you say a "totally unpolarized beam of photons" does that imply a statistical mixture of states? Under the discussion: "What is the difference between entangled and "normal" photons?" another Sci Advisor said that:

"When you discard information about the other particle, you are left with a statistical mixture. (mathematically, this amounts to taking a partial trace)"

A statistical mixture of states is not equivalent to a linear superposition of states.
 
  • #4
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What is entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them.

What is measurement in quantum mechanics?

In quantum mechanics, measurement refers to the process of obtaining information about a quantum system. This can involve observing the position, momentum, or other properties of a particle.

How are entanglement and measurement related?

Entanglement can be seen as a form of measurement in quantum mechanics, as it allows for the observation of one particle to affect the state of another particle instantaneously, without any physical interaction.

Can entanglement be used for communication?

While entanglement allows for instantaneous communication between particles, it cannot be used for communication between two people. This is because the state of the particles cannot be controlled, and therefore no meaningful message can be sent.

What are the implications of entanglement in quantum computing?

Entanglement is a crucial concept in quantum computing, as it allows for the creation of quantum bits (qubits) that can store and process information in a superposition of states. This enables quantum computers to perform certain tasks much faster than classical computers.

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