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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 do two-way protocols allow to extract entanglement from states like Werner's?

As discussed in [Lo and Popescu 1999], it is always possible to distill entanglement from pure bipartite states using a one-way protocol. The gist of the idea, as I understand it, is Proposition 1 in ...
glS's user avatar
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Two Quantum State Density Matrices with Unequal Off-Diagonal Elements but Equal Magnitudes

I recently read Kitaev's paper on magic state distillation. I want to verify whether the circuit for the [5,1,3] encoder can map a single qubit state T_0 to the logical state T_1 in the encoded space. ...
Xiao H's user avatar
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Does the preparation of magic states need magic gates?

It is well known that universal quantum computation needs magic states. So we need to prepare magic states although it is noisy. My question is does the preparation of magic states needs magic gates?
Michael.Andy's user avatar
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Magic state distillation of physical vs logical qubit

In the original paper by Bravyi and Kitaev, the distillation procedure takes 5 physical qubits, each prepared in a faulty T state. The qubits are in a product state, and error can be detected by ...
David Dentelski's user avatar
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15-to-1 distillation protocol in lattice surgery: doesn't the potential rejection of the level-1 magic states makes it last longer than $15$ timestep?

Overview of my question I am following Litinsky's paper, and I would like to better understand how the duration of the level-2 15-to-1 distillation protocol is being estimated. Litinsky's says that it ...
Marco Fellous-Asiani's user avatar
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15-to-1 distillation protocol implemented with lattice surgery: don't we loose transversality by commuting Clifford toward measurements?

I am following Litinsky's paper explaining the 15-to-1 distillation protocol. The usual "trick" done to distill, say the $|T \rangle \equiv T |+ \rangle$ magic state, is to use a code ...
Marco Fellous-Asiani's user avatar
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15-to-1 distillation protocol: why is the probability of error of the distilled state $35p^3$ and not $\binom{15}{3} p^3=455p^3$?

The circuit performing the $15$-to-$1$ distillation of the magic state $T|+\rangle$ is shown below (figure taken from Litinski's paper). The first gates encode the $|+\rangle$ of the 15 qubit code. A ...
Marco Fellous-Asiani's user avatar
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1 answer
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Injecting arbitrary rotations into the surface code

I'm trying to find an exact resource count for specific QFTs. A QFT generally needs small power-of-two rotations. These can be constructed out of Clifford+T, but I'm wondering if one can inject them ...
Sam Jaques's user avatar
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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 Wooters. The idea (I think) is that $k$...
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How to perform a multi Pauli rotation with arbitary angle?

Recently, I was trying to find some methods to perform a multi Pauli rotation gate with arbitary angle. I want to use the method proposed in the paper arXiv:1808.02892v3, and the circuit is shown as ...
Zehong Fan's user avatar
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How to prove that the distillable entanglement satisfies $E_D(|\psi_d\rangle\!\langle\psi_d|)\ge \log d$?

If I have a pure state vector: $$ \left|\psi_d\right\rangle=\frac{1}{\sqrt{d}}\sum^{d}_{i=1}\left|ii\right\rangle $$ then the distillable entanglement satisfies: $$ E_{D}(\left|\psi_d\right\rangle\...
MZperX's user avatar
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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. ...
Bentanglement's user avatar
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Equivalence between entanglement purification and quantum error correction

I've recently been reading the seminal paper recently (BDSW 1996), where they established the equivalence between 1-EPP (one-way classical communication) and error correction through explicit ...
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Under what conditions does entanglement distillation work?

The picture below shows the two protocols to distill EPR pairs and enhance the fidelity. EDIT: I am trying to understand under what conditions such a protocol achieve the task, when repetead a number ...
Daniele Cuomo's user avatar
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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:...
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Necessity for discarding errored magic state distillation

The magic state distillation process ends with measuring the state of a logical qubit that is encoded in many (for example 15) data qubits. Why does the distillation needs to be discarded and repeated ...
Yaniv Kurman's user avatar
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How are the singlets distilled in Bennett et al.'s 1995 protocol?

Context --- $\newcommand{\ket}[1]{|#1\rangle}$In (Bennett et al. 1995) the authors present a scheme to concentrate entanglement from a given pure bipartite state via LOCCs. More precisely, given a ...
glS's user avatar
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How can one impliment Bennett's partial measurement onto a binomial subspace for state distillation?

I'm reading the seminal paper on entanglement distillation by Bennett et. al. The idea is that Alice and Bob have $n$ identical copies of an imperfect (but pure) Bell state. The initial state is ...
Visipi's user avatar
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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 ...
Marco Fellous-Asiani's user avatar
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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 ...
user15342's user avatar
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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 ...
metkuma12's user avatar
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What is the deep physical reason behind the existence of bound entanglement? [closed]

In Quantum Information processing, we can extract entanglement from $n$-copies of a weakly entangled state to produce a fully or highly entangled states in $d$-dimensions, using the known distillation ...
Devjyoti Tripathy's user avatar
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What is the intuition behind the following entanglement distillation protocol for continuous variable systems?

The protocol is: We start with a supply of identically prepared bipartite non-Gaussian states. The overall protocol then amounts to an iteration of the following basic steps. The states will be mixed ...
Devjyoti Tripathy's user avatar
4 votes
1 answer
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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 $\rho^{\otimes N}$ ...
glS's user avatar
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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 $1$-...
Sanchayan Dutta's user avatar
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1 answer
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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^{\...
Sanchayan Dutta's user avatar
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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-...
Paul B. Slater's user avatar
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1 answer
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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 ...
EnthusiastiC's user avatar
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1 answer
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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 ...
user120404's user avatar
21 votes
1 answer
532 views

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 ...
Emily Tyhurst's user avatar