Multipartite Quantum Systems Research Articles

Completely entangled subspaces from Moore-like matrices

Construction of completely entangled subspaces (CES) has gained a considerable attention, recently. These subspaces which contain only entangled states are of great importance for entanglement theory and also provide a valuable resource for quantum information processing tasks. The results of [Proc. Math. Sci., 114, 365 (2004)] and in particular using the properties of certain matrix, namely Vandermonde matrix, to build CES motivated us to search for new distinct CES's. Mainly, the stimulating question of whether there are other matrices that can lead to building CESs emerged. In the current paper we give an affirmative answer to this question by providing a method for constructing CESs using the properties of Moore-like matrices. In addition, we give few examples for the proposed subspaces in case of 3-qubit and 2-qutrit systems. Then a comparison between the resulted subspaces and those constructed from Vandermonde matrix has been given for the systems understudy. The results shows that the two methods give identically the same subspaces in case of multiqubit systems. However, for multipartite systems with local dimensions d ≥ 3 the two methods gave unequivalent CES subspaces. Interestingly, the properties of the proposed Moore-like matrices provided a far rich way for constructing CES subspaces. It leads to generating as many distinct CES's as we want for each multipartite quantum system. This is in contrary to Vandermonde-based method which can give only one CES per system. In addition, the basis for each of the given examples has been obtained in a simple form. Moreover, we evaluated the entanglement of uniformly mixed states over the obtained subspaces in terms of concurrence and geometric measure of entanglement. Since different parameters of a Moore-like matrix lead to distinct CESs for the same system, the realized results can open the door for more investigations and/or applications.

On the relation between the subadditivity cone and the quantum entropy cone

Given a multipartite quantum system, what are the possible ways to impose mutual independence among some subsystems, and the presence of correlations among others, such that there exists a quantum state which satisfies these demands? This question and the related notion of a pattern of marginal independence (PMI) were introduced in [1], and then argued in [2] to be central in the derivation of the holographic entropy cone. Here we continue the general information theoretic analysis of the PMIs allowed by strong subadditivity (SSA) initiated in [1]. We show how the computation of these PMIs simplifies when SSA is replaced by a weaker constraint, dubbed Klein’s condition (KC), which follows from the necessary condition for the saturation of subadditivity (SA). Formulating KC in the language of partially ordered sets, we show that the set of PMIs compatible with KC forms a lattice, and we investigate several of its structural properties. One of our main results is the identification of a specific lower dimensional face of the SA cone that contains on its boundary all the extreme rays (beyond Bell pairs) that can possibly be realized by quantum states. We verify that for four or more parties, KC is strictly weaker than SSA, but nonetheless the PMIs compatible with SSA can easily be derived from the KC-compatible ones. For the special case of 1-dimensional PMIs, we conjecture that KC and SSA are in fact equivalent. To make the presentation self-contained, we review the key ingredients from lattice theory as needed.

Locally distinguishing nonlocal sets with entanglement resource

Recently, much attention has been paid to the construction of nonlocal sets. The existence of nonlocal sets gives rise to the research on the entanglement-assisted discrimination. We first present a method to locally distinguish a nonlocal set of orthogonal product states in (ℂd)⊗n by utilizing only a 2⊗2 maximally entangled state. Then we generalize the method to general multipartite quantum system ⊗i=1nℂdi based on the same entangled resource. Fortunately, we find that a 2⊗2 maximally entangled state can be employed as a universal resource for perfectly distinguishing the nonlocal sets constructed by Zhen et al (2022). In particular, the protocols we designed could not only efficiently distinguish these states, but also show that the strength of these nonlocal sets is minimal from the perspective of auxiliary resources.

Ontological indistinguishability as a central tenet of quantum theory.

Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, the concomitant quantum statistics and their entanglement. Here, we analyse the role of indistinguishability and non-individuality in other areas of quantum theory. We start by analysing how a very peculiar use of indistinguishability underlies Feynman's rules for summing amplitudes in interference phenomena. Next, we study how quantum indistinguishability is underestimated in several topics of debate in the quantum physics literature, such as the Einstein-Podolsky-Rosen argument, Bell's inequalities and the Bell-Kochen-Specker theorem. Finally, we argue that an ontology of truly indistinguishable entities can serve as a basis for a quantum ontology that can give interesting answers to the interpretational problems of quantum mechanics. We claim that, in addition to superposition, contextuality and entanglement, indistinguishability (understood in a robust ontological sense) is one of the central features of quantum physics. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Dynamics of a multipartite hybrid quantum system with beamsplitter, dipole–dipole, and Ising interactions

The possibility of exploiting heterogeneous quantum systems to high precision, for storing, processing, and transmitting information, makes them ideal candidates for multitasking purposes in quantum communication. Appropriate quantum systems involving a judicious choice of interactions that augment each other are potentially useful for probing deep into quantum regimes. Here, we use one such hybrid bipartite quantum model, with one subsystem made of a pair of qubits and another comprising a pair of oscillators, to study the entanglement dynamics and the entanglement transfer between discrete and continuous variables. The basic model is the standard double Jaynes–Cummings model, which, under suitable conditions, is known to support both entanglement transfer and entanglement sudden death. In this work, we generalize this model to include further experimentally relevant interactions, such as the beamsplitter-type exchange interaction between the oscillators, and dipole–dipole and Ising-type interactions between the qubits. The way various interactions and initial oscillator states affect the entanglement dynamics is examined theoretically for generic experimental conditions. Using exact analytical solutions, we show that, compared to the beamsplitter or dipole–dipole interaction, the Ising interaction can have a significant positive impact on entanglement sudden death and birth, and the postponement of the onset of these phenomena, apart from producing a substantial reduction in the time duration of the death.

Completable sets of orthogonal product states with minimal nonlocality

Since the theory of quantum nonlocality without entanglement was proposed, great achievements have been made in the local distinguishability of bipartite orthogonal quantum states, but there are still many unresolved problems. In this paper, we first propose the concept of minimal nonlocality to characterize the lower bound of the amount of the elements contained in a nonlocal set of orthogonal product states. A nonlocal set of orthogonal product states has minimal nonlocality if and only if the set can be distinguished by local operations and classical communication (LOCC) after only a certain state of the set is removed. Then we give a novel method to construct completable sets with minimal nonlocality in bipartite quantum system. Compared with the existing results, the completable sets we construct have the least number of elements in the same quantum systems. Finally, we extend our construction method of completable nonlocal set with fewer elements in bipartite system to tripartite or even more multipartite quantum systems.

Reconstructing the multiphoton spatial wave function with coincidence wave-front sensing

The quantum wave function of multiple particles provides additional information which is inaccessible to detectors working alone. Here, we introduce the coincidence wavefront sensing (CWS) method to reconstruct the phase of the multiphoton transverse spatial wave function. The spatially resolved coincidence photon counting is involved. Numerical simulations of two-photon cases using the weak measurement wavefront sensor are performed to test its correctness, and the phase information hidden in the correlation are revealed. Our work provides a direct spatial way to characterize multipartite quantum systems, and leads to fundamental studies like experimental Bohmian mechanics and applications in quantum optical technologies.

Observation of entanglement transition of pseudo-random mixed states

Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.

Principle of Information Causality Rationalizes Quantum Composition.

The principle of information causality, proposed as a generalization of no signaling principle, has efficiently been applied to outcast beyond quantum correlations as unphysical. In this Letter, we show that this principle, when utilized properly, can provide physical rationale toward structural derivation of multipartite quantum systems. In accordance with the no signaling condition, the state and effect spaces of a composite system can allow different possible mathematical descriptions, even when descriptions for the individual systems are assumed to be quantum. While in one extreme, namely, the maximal tensor product composition, the state space becomes quite exotic and permits composite states that are not allowed in quantum theory, the other extreme-minimal tensor product composition-contains only separable states, and the resulting theory allows only Bell local correlation. As we show, none of these compositions is commensurate with information causality, and hence cannot be the bona-fide description of nature. Information causality therefore promises an information-theoretical derivation of self duality of the state and effect cones for composite quantum systems.

Experimental Activation of Strong Local Passive States with Quantum Information.

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.

The Tensor Harish-Chandra–Itzykson–Zuber Integral II: Detecting Entanglement in Large Quantum Systems

We consider the recently introduced generalization of the Harish-Chandra–Itzykson–Zuber integral to tensors and discuss its asymptotic behavior when the characteristic size N of the tensors is taken to be large. This study requires us to make assumptions on the scaling with N of the external tensors. We analyze a two-parameter class of asymptotic scaling ansätze, uncovering several non-trivial asymptotic regimes. This study is relevant for analyzing the entanglement properties of multipartite quantum systems. We discuss potential applications of our results to this domain, in particular in the context of randomized local measurements.

Tighter Monogamy Relations for Concurrence and Negativity in Multiqubit Systems

The entanglement in multipartite quantum system is hard to characterize and quantify, although it has been intensively studied in bipartite systems. The monogamy of entanglement, as a special property of multipartite systems, shows the distribution of entanglement in the system. In this paper, we investigate the monogamy relations for multi-qubit systems. By using two entangled measures, namely the concurrence C and the negativity Nc, we establish tighter monogamy inequalities for their α-th power than those in all the existing ones. We also illustrate the tightness of our results for some classes of quantum states.

On monogamy and polygamy relations of multipartite systems

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems in a unified manner. It is known that any bipartite measure obeys monogamy and polygamy relations for the r-power of the measure. We show in a uniformed manner that the generalized monogamy and polygamy relations are transitive to other powers of the measure in weighted forms We demonstrate that our weighted monogamy and polygamy relations are stronger than recently available relations. Comparisons are given in detailed examples which show that our results are stronger in both situations.

Quantum superposition of causal structures as a universal resource for local implementation of nonlocal quantum operations

Spatial separation restricts the set of locally implementable quantum operations on distributed multipartite quantum systems. We propose that indefinite causal structure arising due to quantum superposition of different space-time geometries can be used as an independent universal resource for local implementation of any quantum operation on spatially distributed quantum systems. Consequently, all such quantum tasks that are not accomplishable by local operations and classical communication (LOCC) only also become locally accomplishable. We show that exploiting indefinite causal structure as the sole resource, it is possible to perfectly teleport the state of one agent's subsystem to the other distant laboratory in such a way that the agent at the distant laboratory can have access to the whole initially shared state in his or her laboratory and can perform any global quantum operation on the joint state locally. We further find that, after the teleportation process, the resource -- indefinite causal structure of the space-time does not get consumed. Hence, after implementing the desired quantum operation the state of the first agent's subsystem can be teleported back to its previous laboratory using the same resource. We show that this two-way teleportation is not always necessary for locally executing all nonlocal quantum tasks that are not realisable by LOCC only. Without invoking any kind of teleportation, we present a protocol for perfect local discrimination of the set of four Bell states that exploits indefinite causal structure as the sole resource. As immediate upshots, we present some more examples of such nonlocal tasks as local discrimination of the set of states exhibiting ``quantum nonlocality without entanglement" and activation of bound entangled states that are also achievable by our proposed protocol incorporating indefinite causal structure as a resource.

Quantum information masking of an arbitrary unknown state can be realized in the multipartite lower-dimensional systems

Quantum information masking is a protocol that hides the original quantum information from subsystems and spreads it over quantum correlation, which is available to multipartite except bipartite systems. In this work, we explicitly study the quantum information masking in multipartite scenario and prove that there exists an universal quantum masker can mask the information encoding in the unknown states into a multipartite system with lower-dimensional local systems, namely, all the k-level quantum states can be masked into a m-qudit systems (m ≥ 4) whose local dimension d ≤ k . In order to observe the masking process intuitively, explicitly controlled operations are provided. Our scheme well demonstrates the abundance of quantum correlation between multipartite quantum system and has potential application in the security of quantum information processing.

Global and Bipartite Entanglement for Three-Qubit System Local Unitary Classes

Entanglement of multipartite quantum systems is an important resource in the field of quantum information processing. Using a measure of global entanglement and the notion of concurrence, the properties of entanglement for a three-qubit system are studied and classified in terms of local unitary classes. The connection of such classification with the three-qubit entanglement polytope is also discussed.

Entanglement measures for two-particle quantum histories

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. The proposed approach highlights the utility of using a separable basis for constructing the bipartite quantum histories and allows for quantification of their entanglement from the complete set of experimentally measured sequential weak values. We then illustrate the nonclassical nature of entangled histories with the use of Hardy's overlapping interferometers and explain why local hidden variable theories are unable to correctly reproduce all observable quantum outcomes. Our theoretical results elucidate how the composite tensor product structure of multipartite quantum systems is naturally extended across time and clarify the difference between quantum histories viewed as projection operators in the history Hilbert space and those viewed as chain operators and propagators in the standard Hilbert space.

Nonlocality without entanglement in general multipartite quantum systems

The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon of nonlocality without entanglement more efficiently.

Strong nonlocality with genuine entanglement based on GHZ-like states in multipartite quantum systems

Strong nonlocality with genuine entanglement was first shown by Wang et al using sets of GHZ-like states in tripartite quantum systems (2021 Phys. Rev. A 104, 012 424). However, it is an open problem whether there exists strong nonlocality with genuine entanglement in four or more partite systems. In this paper, we unify two different concepts of strong nonlocality introduced by Halder et al (2019 Phys. Rev. Lett. 122, 040 403) and by Zhang et al (2019 Phys. Rev. A 99, 062108). That is, we use a concept of k-strong nonlocality instead of these two different types of strong nonlocality. A set of orthogonal quantum states is k-strong nonlocal if it is locally irreducible in every k-partition. In fact, the strong nonlocality that is usually said is 2-strong nonlocality. The smaller the k is, the stronger the nonlocality will be. A set of states is k +-strong nonlocal if the strong nonlocality of this set is stronger than k-strong nonlocality but weaker than (k − 1)-strong nonlocality. Based on these concepts, firstly, we show 2-strong nonlocality with genuine entanglement by some sets of GHZ-like states with weight d in tripartite systems. These sets are not necessarily complete bases. Secondly, we present 2-strong nonlocality with genuine entanglement for systems with four or more parties. These results solve the open problem raised by Wang et al Finally, we construct a set of GHZ-like states with n +-strong nonlocality in n-partite quantum systems.

Coherent dynamics in a five-level atomic system

The coherent control of multi-partite quantum systems presents one of the central prerequisites in state-of-the-art quantum information processing. With the added benefit of inherent high-fidelity detection capability, atomic quantum systems in high-energy internal states, such as metastable noble gas atoms, promote themselves as ideal candidates for advancing quantum science in fundamental aspects and technological applications. Using laser-cooled neon atoms in the metastable 3P2 state of state 1s 22s 22p 53s (LS-coupling notation) (Racah notation: 2 P 3/23s[3/2]2) with five m J -sublevels, experimental methods for the preparation of all Zeeman sublevels |m J ⟩ = |+2⟩, |+1⟩, |0⟩, |−1⟩, |−2⟩ as well as the coherent control of superposition states in the five-level system |+2⟩, …, |−2⟩, in the three-level system |+2⟩, |+1⟩, |0⟩, and in the two-level system |+2⟩, |+1⟩ are presented. The methods are based on optimized radio frequency and laser pulse sequences. The state evolution is described with a simple, semiclassical model. The coherence properties of the prepared states are studied using Ramsey and spin echo measurements.