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.
39 questions
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What is the motivation to consider only Z errors in magic state distillation
I have been learning about magic state distillation protocols and there is something I am not understanding correctly. So for the 15-to-1 distillation protocol that can be found in figure 3 in Magic ...
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Entanglement distillation algorithm with increased expected entanglement
$\newcommand{\ket}[1]{\left| #1 \right\rangle}$
Consider an entangled two-qubit state given by
$$
\ket{\psi} = \cos\theta \ket{00} + \sin\theta\ket{11},
$$
i.e., neither $\sin\theta$ nor $\cos\theta$ ...
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Is there an entanglement distillation algorithm that works for arbitrary two-qubit pure states?
$\newcommand{\ket}[1]{\left|#1\right\rangle}$
Consider a pure state of the form
$$
\ket{\psi} = \bigotimes_{n=1}^\infty \ket{\phi},
$$
where $ \ket{\phi} \in \mathcal{H}_A \otimes \mathcal{H}_B $ is ...
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Simulating a full Y or T factory under circuit level noise - figure of merits?
I have written some code that can simulate the logical circuits corresponding to a full T (or Y) factory under circuit level noise in Stim, emulating a memory type experiment with surface code patches....
user29731
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Is entanglement distillation possible between states of different fidelities?
I am looking for an algorithm that allows me to perform distillation from a pair of W-states of different fidelities. All the algorithms I found so far are focused on distilling identical states, ...
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DEJMPS and EXPEDIENT distillation protocols implementation in qiskit
I am new to Qiskit and distillation protocols. I am wondering if there is a tutorial or a link to the implementation of the DEJMPS and EXPEDIENT distillation protocols in Qiskit.
What I want to ...
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Finding stabilizers from a T distillation code
Consider $T$ state distillation as per Figure 14 in this paper.
I am trying to figure out what the stabilizers are. I thought of trying to evolve them starting from e.g. $S = XI\cdots I$ acting on the ...
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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 ...
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Deriving |𝐶𝐶𝑍⟩ magic states from |𝐶𝐶𝐶𝑍⟩?
Analogous to the $|T\rangle$ and $|CCZ\rangle$ magic states, one can define a $|C^n Z\rangle$ magic state. Is there any known quantification of the amount of magic of this state, and is there a way to ...
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How are these T-distillation circuits derived?
I'm trying to wrap my head around T-distillation circuits, specifically for the 15-to-1 distillation code. My question is, how does one discover these circuits from the description of the code?
There ...
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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♦
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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. ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
- 2,151
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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 $...
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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\...
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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. ...
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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 ...
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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 ...
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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♦
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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♦
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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 $1$-...
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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^{\...
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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-...
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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 ...
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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 ...
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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 ...
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