Magic state distillation from entangled states

Bao, Ning; Cao, ChunJun; Su, Vincent Paul

doi:10.1103/physreva.105.022602

Cited by 6 publications

(3 citation statements)

References 61 publications

(72 reference statements)

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“…In particular, it has been reported that the phase-GHZ state with a 𝜋/4 phase can be useful for magic-state distillation. [30] We can prepare the desired phase-GHZ state |PGHZ (4) (𝜃)⟩ with phase 𝜃 by adjusting the local phase of one of the four photons. In this procedure, |PGHZ (4) (𝜃)⟩ can be expressed as the unitary transformation of the |GHZ (4) ⟩ state, with the zero-phase expressed in Equation (3), as follows:…”

Section: Four-photon Ghz State With a Phase From A Warm Atomic Ensemblementioning

confidence: 99%

“…In particular, it has been reported that the phase‐GHZ state with a π/4 phase can be useful for magic‐state distillation. [ 30 ] We can prepare the desired phase‐GHZ state

| {PGH{Z}^{(4)}(\theta )} \rangle

with phase θ by adjusting the local phase of one of the four photons. In this procedure,

| {PGH{Z}^{(4)}(\theta )} \rangle

can be expressed as the unitary transformation of the

| {GH{Z}^{(4)}} \rangle

state, with the zero‐phase expressed in Equation (3), as follows:

$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} \left| {PGH{Z}^{(4)}(\theta )} \right\rangle = U(\theta )\left| {GH{Z}^{(4)}} \right\rangle \\ \quad = \left[ {{{\mathrm{I}}}_1 \oti...

…”

Section: Four‐photon Ghz State With a Phase From A Warm Atomic Ensemblementioning

confidence: 99%

“…[ 29 ] Recently, it has been theoretically shown that entangled states with a phase can be deployed for magic‐state distillation, which in general the entanglement is regarded as a disadvantage for the distillation protocol. [ 30 ] In particular, multipartite GHZ‐type states with phases can improve the success probability of the magic‐state distillation protocol. We also discuss the violation of GBI as an entanglement criterion for four‐photon GHZ states according to the local phase.…”

Section: Introductionmentioning

confidence: 99%

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Violation of Bell Inequality by Four‐Photon Greenberger‐Horne‐Zeilinger State with a Phase from a Warm Atomic Ensemble

Park,

Ryu,

Kim

et al. 2023

Adv Quantum Tech

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A Greenberger–Horne–Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, it is reported that the violations of the general Bell inequality (GBI) introduced in using the four‐photon polarization‐entangled phase‐GHZ state realized via intrinsic polarization correlation and collective two‐photon coherence in the 5S1/2–5P3/2–5D5/2 transition of 87Rb atoms. The phase‐GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the π/4 phase affords maximal violation of the GBI of 2√2 at the local measurement settings of the Pauli operators σx and σy. Strong violations of the GBI of the phase‐GHZ state by 47 standard deviations are experimentally demonstrated. In addition to the entanglement witness for the phase‐GHZ state, the results represent a genuine four‐photon entanglement of the phase‐GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic‐state distillation from entangled states, and quantum networks based on atom–photon interactions.

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Section: Four-photon Ghz State With a Phase From A Warm Atomic Ensemblementioning

confidence: 99%

“…In particular, it has been reported that the phase‐GHZ state with a π/4 phase can be useful for magic‐state distillation. [ 30 ] We can prepare the desired phase‐GHZ state

| {PGH{Z}^{(4)}(\theta )} \rangle

with phase θ by adjusting the local phase of one of the four photons. In this procedure,

| {PGH{Z}^{(4)}(\theta )} \rangle

can be expressed as the unitary transformation of the

| {GH{Z}^{(4)}} \rangle

state, with the zero‐phase expressed in Equation (3), as follows:

$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} \left| {PGH{Z}^{(4)}(\theta )} \right\rangle = U(\theta )\left| {GH{Z}^{(4)}} \right\rangle \\ \quad = \left[ {{{\mathrm{I}}}_1 \oti...

…”

Section: Four‐photon Ghz State With a Phase From A Warm Atomic Ensemblementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Violation of Bell Inequality by Four‐Photon Greenberger‐Horne‐Zeilinger State with a Phase from a Warm Atomic Ensemble

Park,

Ryu,

Kim

et al. 2023

Adv Quantum Tech

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Clifford orbits and stabilizer states

Feng,

Luo

2024

J. Phys. A: Math. Theor.

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Stabilizer states serve as ‘classical objects’ in the stabilizer formalism of quantum theory, and play an important role in quantum error correction, fault-tolerant quantum computation, and quantum communication. They provide an efficient description of many basic features of quantum theory and exhibit a rich structure. For prime dimensional systems, they may be defined by two quite different yet equivalent ways: The first is via stabilizer groups (maximal Abelian subgroups of the discrete Heisenberg–Weyl group). The second is via the orbits of the Clifford group acting on any computational basis state. However, in a general dimensional system, this equivalence breaks down, and consequently, it is desirable to clarify the difference and relation between the above two approaches to stabilizer states. In this work, we show that these two approaches are equivalent if and only if the system dimension is square-free (i.e. has no square factor). Furthermore, we completely reveal the relation between the Clifford orbits and stabilizer states in an arbitrary dimensional system, derive the explicit expressions of the Clifford orbits and determine their cardinalities.

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