Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice--Bob--Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor \textit{ibm\_kingston}, we observe bilocal nonlocality with $\mathcal{S}_{\rm BLHV}=1.067(6)>1$ after readout-error mitigation, while the FNN witnesses reach $99\%$ and $96\%$ of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice--Bob--Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor \textit{ibm\_kingston}, we observe bilocal nonlocality with $\mathcal{S}_{\rm BLHV}=1.067(6)>1$ after readout-error mitigation, while the FNN witnesses reach $99\%$ and $96\%$ of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.

quant-pharXiv:2607.04656Jul 7, 20260 citations

Entangled two-spin qubits

Richard J. Fitzgerald

Physics TodayApr 19, 20120 citations

Representative Geometry of States in the Bilocal Formalism. SU(n) Symmetries from the State-Value Space and Spin Dualism.

Andrzej Tyminski

We consider the bilocal formalism of quantum mechanics, in which the wave functiondefined on the space $Q \times Q$ is interpreted as a description of two statesof the same particle.In contrast to earlier approaches, we do not assume the wave function to be scalar-valued,but instead allow it to take values in a finite-dimensional complex vector space. We show that changing the codomain of the wave function does not modify the structureof the configuration space nor its phase-space realization.The entire bilocal geometry, responsible for the emergence of spacetime,mass, and kinematical spin, remains unchanged.New structures appear exclusively at the level of the state-value space. The space of physical states then takes the form of the complex projective space $\mathbb{C}P^{n-1}$ , which is a natural symplectic manifold and a coadjoint orbitof the group $SU(n)$ .For $n=2$ , the resulting geometry duplicates the structural spin spherealready present in the bilocal formalism, whereas the case $n=3$ leads tothe first non-degenerate representational symmetry. These results suggest that internal symmetries of a representational naturecan be understood as consequences of the geometry of quantum state spaces,rather than as additional postulated degrees of freedom.We consider the bilocal formalism of quantum mechanics, in which the wave functiondefined on the space $Q \times Q$ is interpreted as a description of two statesof the same particle.In contrast to earlier approaches, we do not assume the wave function to be scalar-valued,but instead allow it to take values in a finite-dimensional complex vector space. We show that changing the codomain of the wave function does not modify the structureof the configuration space nor its phase-space realization.The entire bilocal geometry, responsible for the emergence of spacetime,mass, and kinematical spin, remains unchanged.New structures appear exclusively at the level of the state-value space. The space of physical states then takes the form of the complex projective space$\mathbb{C}P^{n-1}$, which is a natural symplectic manifold and a coadjoint orbitof the group $SU(n)$.For $n=2$, the resulting geometry duplicates the structural spin spherealready present in the bilocal formalism, whereas the case $n=3$ leads tothe first non-degenerate representational symmetry. These results suggest that internal symmetries of a representational naturecan be understood as consequences of the geometry of quantum state spaces,rather than as additional postulated degrees of freedom.

Feb 6, 20260 citations

Spin bath decoherence of quantum entanglement

Z. Gedik

arXiv:quant-ph/0505176Solid State CommunicationsMar 4, 200619 citations

Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays

Robert E. Throckmorton, S. Das Sarma

We determine the interqubit crosstalk- and charge-noise-induced decoherence time ${T}_{2}^{*}$ for a system of $L$ exchange-coupled electronic spin qubits in arrays of size $L=3$ --14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that ${T}_{2}^{*}$ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring ${T}_{2}^{*}$ . A key finding is that ${T}_{2}^{*}$ decreases with increasing $L$ . We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.We determine the interqubit crosstalk- and charge-noise-induced decoherence time ${T}_{2}^{*}$ for a system of $L$ exchange-coupled electronic spin qubits in arrays of size $L=3$--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that ${T}_{2}^{*}$ depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring ${T}_{2}^{*}$. A key finding is that ${T}_{2}^{*}$ decreases with increasing $L$. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.

arXiv:2112.08358Physical review. B./Physical review. BJun 21, 202215 citations

\mathcal{S}_{\rm BLHV}=1.067(6)>1

after readout-error mitigation, while the FNN witnesses reach

99\%

and

96\%

of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.

We consider the bilocal formalism of quantum mechanics, in which the wave functiondefined on the space

Q \times Q

is interpreted as a description of two statesof the same particle.In contrast to earlier approaches, we do not assume the wave function to be scalar-valued,but instead allow it to take values in a finite-dimensional complex vector space. We show that changing the codomain of the wave function does not modify the structureof the configuration space nor its phase-space realization.The entire bilocal geometry, responsible for the emergence of spacetime,mass, and kinematical spin, remains unchanged.New structures appear exclusively at the level of the state-value space. The space of physical states then takes the form of the complex projective space

\mathbb{C}P^{n-1}

, which is a natural symplectic manifold and a coadjoint orbitof the group

SU(n)

.For

n=2

, the resulting geometry duplicates the structural spin spherealready present in the bilocal formalism, whereas the case

n=3

leads tothe first non-degenerate representational symmetry. These results suggest that internal symmetries of a representational naturecan be understood as consequences of the geometry of quantum state spaces,rather than as additional postulated degrees of freedom.

We determine the interqubit crosstalk- and charge-noise-induced decoherence time

{T}_{2}^{*}

for a system of

L

exchange-coupled electronic spin qubits in arrays of size

L=3

--14 for a number of different multiqubit geometries by directly calculating the return probability. We compare the behavior of the return probability to other quantities, namely, the average spin, the Hamming distance, and the entanglement entropy. In all cases, we use a starting state with alternating spins, $|{\mathrm{\ensuremath{\Psi}}}_{0}\ensuremath{\rangle}=|\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\downarrow}\ensuremath{\cdots}\ensuremath{\rangle}$. We show that a power law behavior, ${T}_{2}^{*}\ensuremath{\propto}{L}^{\ensuremath{-}\ensuremath{\gamma}}$, is a good fit to the results for the chain and ring geometries as a function of the number of qubits and provide numerical results for the exponent $\ensuremath{\gamma}$. We find that

{T}_{2}^{*}

depends crucially on the multiqubit geometry of the system. We also calculate the expectation value of one of the spins, the Hamming distance, and the entanglement entropy and show that they are good proxies for the return probability for measuring

{T}_{2}^{*}

. A key finding is that

{T}_{2}^{*}

decreases with increasing

L

. We also demonstrate that these results may be understood in terms of perturbation theory and its breakdown.