How to build a pure entangled initial state
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Ivan Huarte
- Posts: 4
- Joined: 06 Oct 2023, 14:37
- Location: Zaragoza, Spain
How to build a pure entangled initial state
Hi!. I wanted to create a pure entangled state between 2 spins, but i dont know how to do it via p_state in MPS.from_product_state because by definition a pure entangled state is not a product state. Does anybody know?
Re: How to build a pure entangled initial state
Hi! The function you want is probably: MPS.from_singlets
Re: How to build a pure entangled initial state
Indeed, Markus is right that singlets are only one example of entangled states. But they're only entangled on pairs of sites, so for more than 2 sites they're "product states" again.
Really, you need to clarify which entangled state you want - there are plenty. For example, you could also use a "random" state according to the Haar measure (which has volume-law entanglement, so only works for small systems), or "random" in the sense of starting form a product state and applying only a short layer of local unitary, random circuits, or other simple "analytical" states like GHZ, AKLT ground states, or or or...
Singlets are maximally entangled states for two spins, but again there are also other maximally entangled states (like the m=0 triplet \(1/2(\ket{\uparrow\downarrow} + \ket{\downarrow\uparrow})\)), or the "identity" \(1/2(\ket{\uparrow\uparrow} + \ket{\downarrow\downarrow})\).
Really, you need to clarify which entangled state you want - there are plenty. For example, you could also use a "random" state according to the Haar measure (which has volume-law entanglement, so only works for small systems), or "random" in the sense of starting form a product state and applying only a short layer of local unitary, random circuits, or other simple "analytical" states like GHZ, AKLT ground states, or or or...
Singlets are maximally entangled states for two spins, but again there are also other maximally entangled states (like the m=0 triplet \(1/2(\ket{\uparrow\downarrow} + \ket{\downarrow\uparrow})\)), or the "identity" \(1/2(\ket{\uparrow\uparrow} + \ket{\downarrow\downarrow})\).