Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [state-distillation]

For questions about the process of transforming multiple copies of a state into Bell pairs using only local operations and classical communication.

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How does magic state distillation overhead scale compare to quantum advantages?

I'm interested in the model of quantum computation by magic state injection, that is where we have access to the Clifford gates, a cheap supply of ancilla qubits in the computational basis, and a few expensive-to-distill magic states (usually those…
Emily Tyhurst
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Good references to learn magic state distillation for fault tolerance

I need to learn magic state distillation procedure and their application to fault-tolerance. One of the original paper on this subject is the following: https://arxiv.org/pdf/quant-ph/0403025.pdf I am wondering if there are more recent and pedagogic…
Marco Fellous-Asiani
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Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in H^{\otimes k}$ of Schimdt-rank at most $2$ such…
Sanchayan Dutta
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Why the perfect 5-qubit code was used for magic state distillation?

I am currently trying to understand magic state distillation. So far, my understanding is that the general idea is to find a code where a non-Clifford gate is transversal (very well explained in https://arxiv.org/pdf/1612.07330.pdf on Fig. 3). For…
Diego
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Entanglement distillation by local operations and post-selection using one entanglement pair

Consider the state $|X\rangle = \sqrt{0.9} |00\rangle + \sqrt{0.1} |11\rangle$, shared between Alice and Bob, who are located far apart. Alice brings in an ancilla qubit at her location (left-most qubit in the kets): $|X\rangle = \sqrt{0.9}…
user120404
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-Schmidt probabilities that members of the sets have…
Paul B. Slater
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What is the difference between "entanglement distillation" and "entanglement purification"?

To my understanding, entanglement distillations is transformation of several copies of weakly entangled states into fewer copies of more strongly entangled states using local operations and classical communication. My question is, what is the…
metkuma12
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Why is $\rho$ NPT if and only if $\rho^{\otimes N}$ is NPT?

In Horodecki et al. (1998), to prove that distillability implies having a negative partial transpose (being NPT). The authors use the fact that "a state $\rho$ is NPT if and only if $\rho^{\otimes N}$ is". A state $\rho$ being "NPT" means here that…
glS
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What do entanglement cost and distillable entanglement have to do with measuring entanglement?

So far what I have learned is that von-Neumann entropy is a tool to measure or quantify information and therefore entanglement for a given pure state system. However, similar concepts emerge from the task of measuring entanglement in general, which…
EnthusiastiC
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What's so bad about preparing magic states by measuring Clifford gates?

Suppose we want to perform a gate from the third level of the Clifford hierarchy for example $ T,CS, CCZ, CCX $. To implement such a gate using gate teleportation we need to take as an input certain ancilla states. For example, a $ |T\rangle $ state…
Ian Gershon Teixeira
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Understanding entanglement distillation via stabilizer codes?

I am having some trouble understanding the distillation of EPR pairs using a stabilizer code. This idea goes back to the paper by Bennet, DiVincenzo, Smolin, and Wootters. The idea (I think) is that $k$-EPR pairs can be distilled via an $[n,k]$…
Condo
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What are good pedagogical introductions to entanglement distillation?

I have a basic understanding of what entanglement distillation entails, up to the typical subspace projection protocol described in Nielsen & Chuang, and I would like to read more on the subject. In particular, I'm interested in protocols that deal…
Bentanglement
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Why does the entanglement entropy give the number of singlets required to create a given state?

I've read that, given a bipartite pure state $|\Phi\rangle$, its entanglement (equivalently here, von Neumann) entropy $E(\Phi)$ gives the asymptotic number of singlets required to create $n$ copies of $|\Phi\rangle$. More specifically, that for all…
user15342
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Geometric interpretation of 1-distillability

This is a sequel to Motivation for the definition of k-distillability Geometrical interpretation from the definition of 1-distillability The eigenstate $|\psi\rangle$ of the partially transposed $1$-distillable states will have Schmidt rank at…
Sanchayan Dutta
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Simulating the $d=5$ colour code magic state cultivation results with $|{\text{cat}_n}\rangle$ states stabiliser decomposition

In the magic state cultivation paper, the authors mentioned: "due to a lack of better alternatives, we are forced to rely on Assumption 3.1." - which is to replace all the $T$ gates in the simulation with $S$ gates instead. However, they proceed to…
VicQ
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