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An analytical condition for the violation of Mermin's inequality by any three qubit state
Quantum Physics · Submitted 8 Feb 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here we derive an analytical formula for the maximum value of the expectation of the Mermin operator in terms of eigenvalues of symmetric matrices, that gives the maximal violation of the Mermin inequality for all three qubit pure and mixed states.
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The abstract, sentence by sentence
Mermin's inequality is the generalization of the Bell-CHSH inequality for three qubit states. The violation of the Mermin inequality guarantees the fact that there exists quantum non-locality either between two or three qubits in a three qubit system. In the absence of an analytical result to this effect, in order to check for the violation of Mermin's inequality one has to perform a numerical optimization procedure for even three qubit pure states. Here we derive an analytical formula for the maximum value of the expectation of the Mermin operator in terms of eigenvalues of symmetric matrices, that gives the maximal violation of the Mermin inequality for all three qubit pure and mixed states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Mermin's inequality is the generalization of the Bell-CHSH inequality for three qubit states. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | The violation of the Mermin inequality guarantees the fact that there exists quantum non-locality either between two or three qubits in a three qubit system. | background 0.83 | 0.07 | 0.07 | asserted 1.00 |
| s2 | In the absence of an analytical result to this effect, in order to check for the violation of Mermin's inequality one has to perform a numerical optimization procedure for even three qubit pure states. | gap 1.00 | 0.06 | 0.04 | asserted 1.00 |
| s3 | Here we derive an analytical formula for the maximum value of the expectation of the Mermin operator in terms of eigenvalues of symmetric matrices, that gives the maximal violation of the Mermin inequality for all three qubit pure and mixed states. | contribution 0.94 | 0.97 | 0.94 | asserted 1.00 |
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The paper
Original abstract
Mermin's inequality is the generalization of the Bell-CHSH inequality for three qubit states. The violation of the Mermin inequality guarantees the fact that there exists quantum non-locality either between two or three qubits in a three qubit system. In the absence of an analytical result to this effect, in order to check for the violation of Mermin's inequality one has to perform a numerical optimization procedure for even three qubit pure states. Here we derive an analytical formula for the maximum value of the expectation of the Mermin operator in terms of eigenvalues of symmetric matrices, that gives the maximal violation of the Mermin inequality for all three qubit pure and mixed states.
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How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 1 paper
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The operator $O$ given in ([ref]) can be obtained by suitably choosing the unit vectors in Mermin operator, which is defined as [ref] [equation] where $â_j$, $b_j$ $(j=1,2,3)$ are the measurement direction for the $j$th party and $σ⃗=(σ_x,σ_y,σ_z)$ are the usual Pauli matrices.
Distinguishing different classes of entanglement of three-qubit pure states · Tangle and it's observable measure · 0.87
Cites it as background 1 paper
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Recently, analytical conditions to estimate the maximal violation of Mermin's inequality for three qubits were proposed [ref] .
Conditional quantum nonlocality in dimeric and trimeric arrays of organic molecules · PBI trimer nonlocal states · 0.82
What it cites
Cites as background 1 paper
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A notable direction in this context is the so-called `superactivation of nonlocality' [ref] which has been investigated also for the case of three qubits [ref] .
Revealing Hidden Genuine Tripartite Nonlocality · Introduction · 0.90
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