Pairwise tomography networks for many-body quantum systems

García-Pérez, Guillermo; Rossi, Matteo A. C.; Sokolov, Boris; Borrelli, Elsi-Mari; Maniscalco, Sabrina

doi:10.1103/physrevresearch.2.023393

Cited by 23 publications

(24 citation statements)

References 45 publications

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“…One of the most prominent examples is the 2-body N -representability problem, where one asks which 2-body reduced density matrices can result as the marginals of a global state of N particles, a problem motivated by the calculation of ground states of 2-body, usually local, Hamiltonians, see for instance [1,2]. Because of its relevance, the SMP has been studied from many different viewpoints, for instance in the context of entanglement [3,4] or Bell non-locality detection [5,6], or by constructing efficient measurement strategies for the estimation of marginal states [7][8][9].…”

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confidence: 99%

Quantum Channel Marginal Problem

Hsieh,

Lostaglio,

Acín

2021

Preprint

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Given a set of local dynamics, are they compatible with a global dynamics? We systematically formulate these questions as quantum channel marginal problems, which can be understood as a dynamical generalization of the marginal problems for quantum states. After defining the notion of compatibility between global and local dynamics, we provide a necessary and sufficient condition for it, showing that it takes the form of a semidefinite program. Using this formulation, we construct channel incompatibility witnesses and show that a set of local channels are incompatible if and only if they demonstrate an advantage in a state-discrimination task.

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confidence: 99%

Quantum Channel Marginal Problem

Hsieh,

Lostaglio,

Acín

2021

Preprint

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“…This representation is particularly useful for systems which do not possess translational invariance, wherein the properties of such correlations do not depend on the distance between the particles only. Moreover, these networks can be obtained efficiently in experimental scenarios, requiring only a logarithmic amount of measurement settings in the system size [34][35][36].…”

Section: Discussionmentioning

confidence: 99%

“…Many relevant physical properties of these states can be inferred from two-body -or pairwisequantities, such as correlators of the form σ l i σ m j , where σ l i and σ m j are Pauli operators with i, j ∈ {x, y, z} (l and m are spin indices), or quantifiers of bipartite entanglement like concurrence [32,33]. Importantly, efficient techniques for performing two-body tomography have been very recently discovered, making all these pairwise quantities experimentally accessible even for large N [34][35][36]. Furthermore, limiting our attention to pairwise quantities naturally leads to a complex network description of the quantum state, and consequently allows us to borrow tools and techniques from classical complex network theory for studying quantum many-body systems.…”

Section: Complex Quantum Network Representationmentioning

confidence: 99%

Emergent entanglement structures and self-similarity in quantum spin chains

Sokolov,

Rossi,

García-Pérez

et al. 2020

Preprint

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We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localised communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding, and description of new physical phenomena even in models studied for decades.

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“…In this section, we outline the main points of the method that we propose for assessing level-I entanglement structures, while avoiding technical details when possible. Essentially, our approach exploits the recently proposed partial tomography, in which one reconstructs reduced density operators of the system [19][20][21], rather than attempting the often prohibitive full state tomography, along with the following simple observation.…”

Section: Methodsmentioning

confidence: 99%

Experimentally accessible non-separability criteria for multipartite entanglement structure detection

García-Pérez¹,

Kerppo²,

Rossi³

et al. 2021

Preprint

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The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown states. We propose an experimentally accessible and scalable iterative methodology that identifies, on solid statistical grounds, sufficient conditions for nonseparability with respect to certain partitions. In addition, we propose an algorithm to determine the minimal partitions (those that do not admit further splitting) consistent with the experimental observations. We test our methodology experimentally on a 20-qubit IBM quantum computer by inferring the structure of the 4-qubit Smolin and an 8-qubit W states. In the first case, our results reveal that, while the fidelity of the state is low, it nevertheless exhibits the partitioning structure expected from the theory. In the case of the W state, we obtain very disparate results in different runs on the device, which range from non-separable states to very fragmented minimal partitions with little entanglement in the system. Furthermore, our work demonstrates the applicability of informationally complete POVM measurements for practical purposes on current NISQ devices.

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Pairwise tomography networks for many-body quantum systems

Cited by 23 publications

References 45 publications

Quantum Channel Marginal Problem

Quantum Channel Marginal Problem

Emergent entanglement structures and self-similarity in quantum spin chains

Experimentally accessible non-separability criteria for multipartite entanglement structure detection

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