IA Scholar Query: Computable constraints on entanglement-sharing of multipartite quantum states.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgTue, 22 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440An invertible map between Bell non-local and contextuality scenarios
https://scholar.archive.org/work/qhehynnuojbjbku6p6yiegkmwi
We present an invertible map between correlations in any bipartite Bell scenario and behaviours in an indexed family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual behaviours, respectively. Consequently, we find that the membership problem of set of quantum behaviours in a contextuality scenario is undecidable and the set cannot be fully realised using finite dimensional quantum systems. Finally, we find that neither this set, nor its closure, can be the limit of any sequence of computable supersets, due to the result MIP*=RE. In particular, the semidefinite programming hierarchies in the literature cannot converge to the quantum set of behaviours nor its closure.Victoria Wright, Máté Farkaswork_qhehynnuojbjbku6p6yiegkmwiTue, 22 Nov 2022 00:00:00 GMTGeneral stabilizer approach for constructing highly entangled graph states
https://scholar.archive.org/work/mklnt4wt3jcpvorclitiv64gpi
Highly entangled multipartite states such as k-uniform (k-UNI) and absolutely maximally entangled (AME) states serve as critical resources in quantum networking and other quantum information applications. However, there does not yet exist a complete classification of such states, and much remains unknown about their entanglement structure. Here, we substantially broaden the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states. This method in fact constitutes a general recipe for obtaining multipartitite entangled states from classical codes. Furthermore, we show that at least for a large subset of this new class of k-UNI states, the states are inequivalent under stochastic local operations and classical communication. This subset is defined by an iterative procedure for constructing a hierarchy of k-UNI graph states.Zahra Raissi, Adam Burchardt, Edwin Barneswork_mklnt4wt3jcpvorclitiv64gpiTue, 22 Nov 2022 00:00:00 GMTTesting symmetry on quantum computers
https://scholar.archive.org/work/glfly3jqrfamriobfdeu3bfe7y
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian realizing a time evolution are not useful for timekeeping during that evolution, and bipartite states that are highly extendible are not strongly entangled and thus not useful for basic tasks like teleportation. Motivated by this perspective, this paper details several quantum algorithms that test the symmetry of quantum states and channels. For the case of testing Bose symmetry of a state, we show that there is a simple and efficient quantum algorithm, while the tests for other kinds of symmetry rely on the aid of a quantum prover. We prove that the acceptance probability of each algorithm is equal to the maximum symmetric fidelity of the state being tested, thus giving a firm operational meaning to these latter resource quantifiers. Special cases of the algorithms test for incoherence or separability of quantum states. We evaluate the performance of these algorithms on choice examples by using the variational approach to quantum algorithms, replacing the quantum prover with a parameterized circuit. We demonstrate this approach for numerous examples using the IBM quantum noiseless and noisy simulators, and we observe that the algorithms perform well in the noiseless case and exhibit noise resilience in the noisy case. We also show that the maximum symmetric fidelities can be calculated by semi-definite programs, which is useful for benchmarking the performance of these algorithms for sufficiently small examples. Finally, we establish various generalizations of the resource theory of asymmetry, with the upshot being that the acceptance probabilities of the algorithms are resource monotones and thus well motivated from the resource-theoretic perspective.Margarite L. LaBorde, Soorya Rethinasamy, Mark M. Wildework_glfly3jqrfamriobfdeu3bfe7yThu, 17 Nov 2022 00:00:00 GMTBounding entanglement wedge cross sections
https://scholar.archive.org/work/f6rgvghydncr3avv7aoazgj2ou
The entanglement wedge cross sections (EWCSs) are postulated as dual gravity probes to certain measures for the entanglement of multiparty systems. We test various proposed inequalities for EWCSs. As it turns out, contrary to expectations, the EWCS is not clearly monogamous nor polygamous for tripartite systems but the results depend on the details and dimensionality of the geometry of the gravity solutions. We propose weaker monogamy relations for dual entanglement measures, which lead to a new lower bound on EWCS. Our work is based on a plethora of gravity backgrounds: pure anti de Sitter spaces, anti de Sitter black branes, those induced by a stack of Dp-branes, and cigar geometries in generic dimension.Parul Jain, Niko Jokela, Matti Jarvinen, Subhash Mahapatrawork_f6rgvghydncr3avv7aoazgj2ouMon, 14 Nov 2022 00:00:00 GMTTheoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
https://scholar.archive.org/work/ilc4z3crpff6lnjr64bqjpsety
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., the group of symmetry S_n), and show how to build S_n-equivariant QNNs. We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides the first theoretical guarantees for equivariant QNNs, thus indicating the extreme power and potential of GQML.Louis Schatzki, Martin Larocca, Quynh T. Nguyen, Frederic Sauvage, M. Cerezowork_ilc4z3crpff6lnjr64bqjpsetyMon, 14 Nov 2022 00:00:00 GMTReversible computation and the causal structure of space-time
https://scholar.archive.org/work/zc6tlkcjirdw3dwtcd3pwrvkxy
Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit. The reversible operations that a quantum computer can perform on a qubit are group of linear unitary transformations. However, laws of quantum mechanics prohibit implementation of anti-linear anti-unitary gates, even though they are perfectly reversible. Here we show that such a restriction on possible set of reversible operations is, remarkably, a fundamental constraint of spacetime structure. In particular, it will be shown that construction of any anti-linear anti-unitary gate will lead to violation of a fundamental causal primitive which, as we shall argue, is fundamentally different from the principle of relativistic causality.Anandamay Das Bhowmik, Preeti Parasharwork_zc6tlkcjirdw3dwtcd3pwrvkxyFri, 11 Nov 2022 00:00:00 GMTInflation: a Python library for classical and quantum causal compatibility
https://scholar.archive.org/work/l6aiy4aknjaktihdgmmv3ez3pq
We introduce Inflation, a Python library for assessing whether an observed probability distribution is compatible with a causal explanation. This is a central problem in both theoretical and applied sciences, which has recently witnessed important advances from the area of quantum nonlocality, namely, in the development of inflation techniques. Inflation is an extensible toolkit that is capable of solving pure causal compatibility problems and optimization over (relaxations of) sets of compatible correlations in both the classical and quantum paradigms. The library is designed to be modular and with the ability of being ready-to-use, while keeping an easy access to low-level objects for custom modifications.Emanuel-Cristian Boghiu and Elie Wolfe and Alejandro Pozas-Kerstjenswork_l6aiy4aknjaktihdgmmv3ez3pqTue, 08 Nov 2022 00:00:00 GMTDistinguishability-based genuine nonlocality with genuine multipartite entanglement
https://scholar.archive.org/work/vlzd4llbqzbwjkeuzmtgltamrq
A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular "strong nonlocality" in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a special type of genuinely multipartite entangled states -- the Greenberger-Horne-Zeilinger (GHZ)-like states. We first show that any 5 states of the three-qubit GHZ basis are genuinely nonlocal, while any 4 states of them are not. Then for more general tripartite systems, we present a universal bound about the cardinality for an arbitrary set of GHZ-like states to be genuinely nonlocal. Although not necessary, entanglement is believed to raise difficulty in state discrimination in many situations. In the literature, there has been lots of studies in favor of this perspective, including the efforts seeking for small nonlocal sets consisting of maximally entangled states in bipartite systems. Here in the tripartite case, where GHZ-like states are studied, we also find the existence of some small genuinely nonlocal sets: we show that the cardinality can scale down to linear in the local dimension d. This result not only substantiates the aforemention perspective in multipartite scenario, but also suggests that there might exist substantial difference between strong nonlocality and the normal distinguishability-based multipartite nonlocality.Zong-Xing Xiong, Mao-Sheng Li, Zhu-Jun Zheng, Lvzhou Liwork_vlzd4llbqzbwjkeuzmtgltamrqFri, 04 Nov 2022 00:00:00 GMTResource Marginal Problems
https://scholar.archive.org/work/pzy3goca4bcenlc6rdsscrd73a
We introduce the resource marginal problems, which concern the possibility of having a resource-free target subsystem compatible with a given collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known marginal problems for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is resource-free incompatible with a target subsystem T if all global states compatible with this set must result in a resourceful state in T. We show that this incompatibility induces a resource theory that can be quantified by a monotone, and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that resource-free incompatibility is equivalent to an operational advantage in some subchannel discrimination task. Through our framework, a clear connection can be established between any marginal problem (that involves some notion of incompatibility) for quantum states and a resource theory for quantum states. In addition, the universality of our framework leads, for example, to further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems as well as entanglement transitivity problems. As a byproduct of our investigation, we obtain the first example showing a form of transitivity of nonlocality as well as steerability for quantum states, thereby answering a decade-old question to the positive.Chung-Yun Hsieh, Gelo Noel M. Tabia, Yu-Chun Yin, Yeong-Cherng Liangwork_pzy3goca4bcenlc6rdsscrd73aFri, 04 Nov 2022 00:00:00 GMTImproving social welfare in non-cooperative games with different types of quantum resources
https://scholar.archive.org/work/tudekvssdjg6zgf2nee4jvsh2u
We investigate what quantum advantages can be obtained in multipartite non-cooperative games by studying how different types of quantum resources can improve social welfare, a measure of the quality of a Nash equilibrium. We study how these advantages in quantum social welfare depend on the bias of the game, and improve upon the separation that was previously obtained using pseudo-telepathic strategies. Two different quantum settings are analysed: a first, in which players are given direct access to an entangled quantum state, and a second, which we introduce here, in which they are only given classical advice obtained from quantum devices. For a given game G, these two settings give rise to different equilibria characterised by the sets of equilibrium correlations Q_corr(G) and Q(G), respectively. We show that Q(G)⊆ Q_corr(G) and, by considering explicit example games and exploiting SDP optimisation methods, provide indications of a strict separation between the social welfare attainable in the two settings. This provides a new angle towards understanding the limits and advantages of delegating quantum measurements.Alastair A. Abbott, Mehdi Mhalla, Pierre Pocreauwork_tudekvssdjg6zgf2nee4jvsh2uThu, 03 Nov 2022 00:00:00 GMTThe connected wedge theorem and its consequences
https://scholar.archive.org/work/ixivavv3avaa3opq6s6atduwfu
In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS_2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in arXiv:1912.05649. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.Alex May, Jonathan Sorce, Beni Yoshidawork_ixivavv3avaa3opq6s6atduwfuThu, 03 Nov 2022 00:00:00 GMTA sufficient family of necessary inequalities for the compatibility of quantum marginals
https://scholar.archive.org/work/2wqm3cqw4rhyfa6omxrw5ehzbe
The quantum marginal problem is concerned with characterizing which collections of quantum states on different subsystems are compatible in the sense that they are the marginals of some multipartite quantum state. Presented here is a countable family of inequalities, each of which is necessarily satisfied by any compatible collection of quantum states. Additionally, this family of inequalities is shown to be sufficient: every incompatible collection of quantum states will violate at least one inequality belonging to the family.Thomas C. Fraserwork_2wqm3cqw4rhyfa6omxrw5ehzbeTue, 01 Nov 2022 00:00:00 GMTFermionic Isometric Tensor Network States in Two Dimensions
https://scholar.archive.org/work/csx7b6csvjbjrfwkmz2yzv4hwy
We generalize isometric tensor network states to fermionic systems, paving the way for efficient adaptations of 1D tensor network algorithms to 2D fermionic systems. As the first application of this formalism, we developed and benchmarked a time-evolution block-decimation (TEBD) algorithm for real-time and imaginary-time evolution. The imaginary-time evolution produces ground-state energies for gapped systems, systems with a Dirac point, and systems with gapless edge mode to good accuracy. The real-time TEBD captures the chiral edge dynamics on the boundary of a Chern insulator.Zhehao Dai, Yantao Wu, Taige Wang, Michael P. Zaletelwork_csx7b6csvjbjrfwkmz2yzv4hwyMon, 31 Oct 2022 00:00:00 GMTCosmological states in loop quantum gravity on homogeneous graphs
https://scholar.archive.org/work/lhmed5ykmrbrbejci64vk4ccbe
We introduce a class of states characterized by proposed conditions of homogeneity and isotropy in loop quantum gravity and construct concrete examples given by Bell-network states on a special class of homogeneous graphs. Such states provide new representations of cosmological spaces that can be explored for the formulation of cosmological models in the context of loop quantum gravity. We show that their local geometry is described in an automorphism-invariant manner by one-node observables analogous to the one-body observables used in many-body quantum mechanics, and compute the density matrix representing the restriction of global states to the algebra of one-node observables. The von Neumann entropy of this density matrix provides a notion of entanglement entropy of a local region which respects automorphism-invariance and can be applied to states involving superpositions of distinct graphs.Bekir Baytas, Nelson Yokomizowork_lhmed5ykmrbrbejci64vk4ccbeFri, 28 Oct 2022 00:00:00 GMTTransformations of Stabilizer States in Quantum Networks
https://scholar.archive.org/work/gonzl4y2ajhjrktaanvyupatuq
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC) transformations among stabilizer states. These transformations arise as a physically motivated extension of local operations in quantum networks with access to bipartite entanglement between some of the nodes of the network. First, we show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation, which describes local Clifford transformations among graph states. Then, we introduce a mathematical framework to study PLC equivalence of stabilizer states, relating it to the classification of tuples of bilinear forms. This framework allows us to study decompositions of stabilizer states into tensor products of indecomposable ones, that is, decompositions into states from the entanglement generating set (EGS). While the EGS is finite up to 3 parties [Bravyi et al., J. Math. Phys. 47, 062106 (2006)], we show that for 4 and more parties it is an infinite set, even when considering party-local unitary transformations. Moreover, we explicitly compute the EGS for 4 parties up to 10 qubits. Finally, we generalize the framework to qudit stabilizer states in prime dimensions not equal to 2, which allows us to show that the decomposition of qudit stabilizer states into states from the EGS is unique.Matthias Englbrecht, Tristan Kraft, Barbara Krauswork_gonzl4y2ajhjrktaanvyupatuqTue, 25 Oct 2022 00:00:00 GMTPurity enhances criteria for correlated quantum network states
https://scholar.archive.org/work/nocrvzp3wfh2xjfuhclrt4rir4
Quantum networks are of high interest nowadays. In short, it is the way how quantum sources distribute particles to different parties in the network. Based on whether the sources are classically correlated or not, a quantum network is called correlated quantum network (CQN) or independent quantum network (IQN). Bundles of tools have been developed recently to determine whether a given quantum state or correlation can arise from IQN or not. In comparison, tools for CQN are rare. We propose a systematic approach based on purity to prompt well-known techniques for IQN to work for CQN. With this approach, we came up with criteria which work even simultaneously for networks with different kinds of topology. We also show that this approach can be further improved with more information, e.g., the exact noise model.Zhen-Peng Xuwork_nocrvzp3wfh2xjfuhclrt4rir4Tue, 25 Oct 2022 00:00:00 GMTUnconditional Proofs-of-Work and Other Possibilities of Thermodynamic Cryptography
https://scholar.archive.org/work/w3blra5xqvgt7e7geiv2mod4hm
In line with advances in recent years about realizing cryptographic functionalities in an information-theoretically secure way from physical phenomena and laws, we propose here to obtain useful tasks from the sole assumption of limited free energy. Specifically, based on that assumption -- resulting in a setting loosely related to Maurer's bounded-storage model -- we derive protocols for unconditional proofs-of-thermodynamical-work, secret sharing of free energy, unforgeable money, and proofs-of-position. While our schemes can be considered classical and not quantum per se, they are resistant against both classes of adversaries.Xavier Coiteux-Roy, Stefan Wolfwork_w3blra5xqvgt7e7geiv2mod4hmMon, 24 Oct 2022 00:00:00 GMTEntanglement and negativity Hamiltonians for the massless Dirac field on the half line
https://scholar.archive.org/work/4dd3qgj3lfdoxlrl4calpoiufi
We study the ground-state entanglement Hamiltonian of several disjoint intervals for the massless Dirac fermion on the half-line. Its structure consists of a local part and a bi-local term that couples each point to another one in each other interval. The bi-local operator can be either diagonal or mixed in the fermionic chiralities and it is sensitive to the boundary conditions. The knowledge of such entanglement Hamiltonian is the starting point to evaluate the negativity Hamiltonian, i.e. the logarithm of the partially transposed reduced density matrix, which is an operatorial characterisation of entanglement of subsystems in a mixed states. We find that the negativity Hamiltonian inherits the structure of the corresponding entanglement Hamiltonian. We finally show how the continuum expressions for both these operators can be recovered from exact numerical computations in free-fermion chains.Federico Rottoli and Sara Murciano and Erik Tonni and Pasquale Calabresework_4dd3qgj3lfdoxlrl4calpoiufiFri, 21 Oct 2022 00:00:00 GMTMeasurement-driven navigation in many-body Hilbert space: Active-decision steering
https://scholar.archive.org/work/2duw2srqlzgrjkb5nmprg6ohwa
The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go. This enables a sped-up performance relative to the passive version of the protocol, where no active adjustments are included. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the greedy accumulation of the cost function, such as the target state fidelity. We show the potential of a significant speedup, employing this greedy approach to a broad family of Matrix Product State targets. For system sizes considered here, an average value of the speedup factor f across this family settles about 20, for some targets even reaching a few thousands. We also identify a subclass of Matrix Product State targets, for which the value of f increases with system size. In addition to the greedy approach, the second wayfinding technique is to map out the available measurement actions onto a Quantum State Machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This State Machine-based approach can be applied to a more restricted set of targets, sometimes offering advantages over the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by f≃3.5, outperforming the greedy protocol for this target.Yaroslav Herasymenko, Igor Gornyi, Yuval Gefenwork_2duw2srqlzgrjkb5nmprg6ohwaFri, 21 Oct 2022 00:00:00 GMTTrading causal order for locality
https://scholar.archive.org/work/6hsccd6vrfezzeazig5afpw7qa
Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and non-entangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order -- the AF/BW process -- can perfectly discriminate the states in a QNLWE ensemble -- the SHIFT ensemble -- with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order. Moreover, we show how multipartite generalizations of the AF/BW process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.Ravi Kunjwal, Ämin Baumelerwork_6hsccd6vrfezzeazig5afpw7qaThu, 20 Oct 2022 00:00:00 GMT