Quantifying tripartite entanglement with entropic correlations

Schneeloch, James; Tison, Christopher C.; Fanto, Michael L.; Ray, Shannon; Alsing, Paul M.

doi:10.1103/physrevresearch.2.043152

Cited by 13 publications

(6 citation statements)

References 23 publications

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“…Those sub-regions with significant correlations would be further subdivided and sampled until we have obtained a coarse-grained approximation of the biphoton joint probability distribution that is sampled at high resolution only where there is significant probability, but without overlooking regions of low probability. Because our tripartite entanglement quantifier (13) entropy, and coarse-graining cannot decrease continuous entropy, we can use these same methods to quantify the tripartite entanglement present in these systems without over-estimating it.…”

Section: Discussion: Proposed Experiments and Technical Challengesmentioning

confidence: 99%

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Nonlinear optics as a source of high-dimensional genuine tripartite entanglement

Schneeloch

Birrittella²,

Tison

et al. 2023

Photonics for Quantum 2023

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We lay down a general scheme to quantify the amount of genuine tripartite entanglement present in the spatial and energy-time degrees of freedom using the correlations naturally present in many such sources. To that end, we test our method using the three-photon states generated in three-party extensions of spontaneous parametric down-conversion, and demonstrate that a substantial amount of spatial and energy-time genuine tripartite entanglement can exist for reasonable experimental sources.

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Section: Discussion: Proposed Experiments and Technical Challengesmentioning

confidence: 99%

“…In, 13 we showed how one could use the correlations present between three D-level quantum systems to begin to quantify the tripartite entanglement present. In particular, we found the relation:…”

Section: Quantifying Entanglement With Correlationsmentioning

confidence: 99%

Nonlinear optics as a source of high-dimensional genuine tripartite entanglement

Schneeloch

Birrittella²,

Tison

et al. 2023

Photonics for Quantum 2023

View full text Add to dashboard Cite

show abstract

“…Here the first minimum is taken over all pure state decompositions of ρ and S i (A), S i (B), S i (C) are the von Neumann entropies of the subsystem A, B and C of |ψ i . It turns out that E f (ρ) equals zero for biseparable states [27], and can be lower bounded by V ρ defined as [56] −S(A|BC…”

Section: Performance On More General Quantum Statesmentioning

confidence: 99%

Certifying unknown genuine multipartite entanglement by neural networks

Chen

Lin

Wei

2023

Quantum Sci. Technol.

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Suppose we have an unknown multipartite quantum state, how can we experimentally ﬁnd out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already NP-Hard to determine whether it is entangled or not. Therefore, it is hard to eﬃciently solve the above problem generally. However, since genuine multipartite entanglement is such a fundamental concept that plays a crucial role in many-body physics and quantum information processing tasks, ﬁnding realistic approaches to certify genuine multipartite entanglement is undoubtedly necessary. In this work, we show that neural networks can provide a nice solution to this problem, where measurement statistics data produced by measuring involved quantum states with local measurement devices serve as input features of neural networks. By testing our models on many speciﬁc multipartite quantum states, we show that they can certify genuine multipartite entanglement very accurately, which even include some new results unknown before. We also exhibit a possible way to improve the eﬃciency of our models by reducing the size of features. Lastly, we show that our models enjoy remarkable robustness against ﬂaws in measurement devices, implying that they are very experiment-friendly.

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“…We assess this as follows: given a proposed factoring C 8 = C 2 ⊗ C 2 ⊗ C 2 , we can consider three bipartite entropies by taking the three factors into two groups in the three possible ways. (There are also more sophisticated tripartite entanglement entropies [10] but we do not consider them here). It is elementary that if two of the three vanish so does the third.…”

Section: Jhep01(2023)082mentioning

confidence: 99%

The smallest interacting universe

Zini

Brown

Freedman

2023

J. High Energ. Phys.

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We study a mechanism by which the most basic structures of quantum physics can emerge from the most meager of starting points, a Hilbert space, lacking any preassigned structure such as a tensor decomposition, and a loss function. In a simple toy model of the universe, we hypothesize a fundamental loss functional for the combined Hamiltonian and quantum state, and then minimize this loss functional by gradient descent. We find that this minimization gives rise to a co-emergence of locality, i.e. a tensor product structure simultaneously respected by both the Hamiltonian and the state, suggesting that locality can emerge by a process analogous to spontaneous symmetry breaking. We discuss the relevance of this program to the arrow of time problem.In our toy model, we interpret the emergence of a tensor factorization as the appearance of individual degrees of freedom within a previously undifferentiated (raw) Hilbert space. Earlier work [5, 6] looked at the emergence of locality in Hamiltonians only, and in that context found strong numerical confirmation of the hypothesis that raw Hilbert spaces of dim = n are unstable and prefer to settle on tensor factorization when n is not prime, expressing, for example, n = pq, and in [6] even primes were seen to “factor” after first shedding a small summand, e.g. 7 = 1 + 2 · 3. This was found in the context of a rather general potential functional F on the space of metrics {gij} on $$ \mathfrak{su} $$ su (n), the Lie algebra of symmetries. This emergence of qunits through operator-level spontaneous symmetry breaking (SSB) may help us understand why the world seems to consist of myriad interacting degrees of freedom. But understanding why the universe has an initial Hamiltonian H0 with a many-body structure is of limited conceptual value unless the initial state, ∣ψ0〉, is also structured by this tensor decomposition. Here we adapt F to become a functional on {g, | ψ0〉} = (metrics) × (initial states), and find SSB now produces a conspiracy between g and ∣ψ0〉, where they simultaneously attain low entropy by jointly settling on the same qubit decomposition. Extreme scaling of the computational problem has confined us to studying ℂ4 breaking to ℂ2 ⊗ ℂ2 and ℂ8 breaking to ℂ2 ⊗ ℂ4 or ℂ2 ⊗ ℂ2 ⊗ ℂ2.

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Quantifying tripartite entanglement with entropic correlations

Cited by 13 publications

References 23 publications

Nonlinear optics as a source of high-dimensional genuine tripartite entanglement

Nonlinear optics as a source of high-dimensional genuine tripartite entanglement

Certifying unknown genuine multipartite entanglement by neural networks

The smallest interacting universe

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