Nonlocal States Research Articles

Braneworlds in f(Q) gravity

We propose a braneworld scenario in a modified symmetric teleparallel gravitational theory, where the dynamics for the gravitational field is encoded in the nonmetricity tensor rather than in the curvature. Assuming a single real scalar field with a sine-Gordon self-interaction, the generalized quadratic nonmetricity invariant $\mathbb{Q}$ controls the brane width while keeping the shape of the energy density. By considering power corrections of the invariant $\mathbb{Q}$ in the gravitational Lagrangian, the sine-Gordon potential is modified exhibiting new barriers and false vacuum. As a result, the domain wall brane obtains an inner structure, and it undergoes a splitting process. In addition, we also propose a non-minimal coupling between a bulk fermion field and the nonmetricity invariant $\mathbb{Q}$. Such geometric coupling leads to a massless chiral fermion bound to the 3-brane and a stable tower of non-localized massive states.

Nonlocal quantum state interferography

Quantum state interferography has recently been proposed as an interference-based technique for the measurement of the general qubit and pure qudit states [Phys. Rev. Lett. 125, 123601 (2020)]. This interferometric method exploits the relationship between the off-diagonal elements of the density matrix and the expectation values of non-Hermitian spin ladder operators. The extension of this method to a composite system is however nontrivial, as it involves the measurement of both single-photon and nonlocal multiphoton interferences. In this work, we present the theoretical analysis of the two-photon quantum state interferography of an arbitrary quantum state. We show that complete state information could in principle be obtained with two measurement settings and by recording six interferograms, using a single-photon sensitive imaging device. We then experimentally demonstrate two-photon nonlocal quantum state interferography of polarization-entangled photon pairs generated with type-I spontaneous parametric down conversion. Quantum state interferography of all four Bell states is performed. An upper bound on the separability of the bipartite states is established in terms of the visibility, phase average intensity, and phase shift of the interference patterns related to the antidiagonal elements of the matrix. Each of the four Bell states can be distinguished by the violation of these bounds uniquely.

Multinode State Transfer and Nonlocal State Preparation via a Unidirectional Quantum Network

Quantum networks with the ability to coherently transfer quantum states between different nodes open up possibilities for upscaling quantum technologies. In this work, we propose a theoretical protocol to implement the multinode state transfer and nonlocal state preparation in a one-dimensional network consisting of many quantum nodes coupled to a common unidirectional channel. By time-dependently modulating the coupling strength between the nodes and the channel, a quantum state stored in one node can be distributed to the other nodes through the channel, while a series of dark-state conditions ensure a desired final state. This protocol can also be used to prepare nonlocal entanglement states of these nodes, such as the W -type state. Importantly, it can be realized in various quantum platforms with currently available technologies.

Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains

Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor—also known as Shiba chains—up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM

This paper studies the dynamics of nonlocal piezo-magnetic nanobeams (PMNBs) embedded in the local/nonlocal viscoelastic medium through the consistent and paradox-free model of the nonlocal theory. Besides, to perform the dynamic analysis, an exact solution and an efficient approach of generalized differential quadrature method (GDQM) are introduced. Since the size-dependency of the uniform loads is wrongly neglected by the nonlocal elasticity in differential form, the size-dependency of piezo-magnetic load is applied through the two-phase theory. Also, size dependency of the viscoelastic medium is accurately applied and examined through the solutions presented employing the differential two-phase theory and satisfying the constitutive boundary conditions. In this regard, the two-phase resultant equations of motions together with boundary conditions including the constitutive ones related to two-phase PMNB and the two-phase medium are attained. To confirm the credibility and efficiency of the extracted equations as well as presented solution procedures, several analogical studies are accomplished, and it is shown that the results obtained from the differential relations are reliable and consistence with those extracted from the integral nonlocal relations. It is shown that the present approach of the GDQM simplifies the solution procedures of the nonlocal problems and improves the precisions in the cases close to the pure nonlocal state. The presented results emphasize that the size-dependency of viscoelastic medium, external electric, and magnetic loads play significant roles on the vibration characteristics, and therefore it must be considered based on two-phase theory. The available results can be helpful to achieve an excellent design of smart nanobeams embedded in viscoelastic medium.

Quantum-Memory-Enhanced Preparation of Nonlocal Graph States.

Graph states are an important class of multipartite entangled states. Previous experimental generation of graph states and in particular the Greenberger-Horne-Zeilinger (GHZ) states in linear optics quantum information schemes is subjected to an exponential decay in efficiency versus the system size, which limits its large-scale applications in quantum networks. Here, we demonstrate an efficient scheme to prepare graph states with only a polynomial overhead using long-lived atomic quantum memories. We generate atom-photon entangled states in two atomic ensembles asynchronously, retrieve the stored atomic excitations only when both sides succeed, and further project them into a four-photon GHZ state. Wemeasure the fidelity of this GHZ state and further demonstrate its applications in the violation of Bell-type inequalities and in quantum cryptography. Our work demonstrates the prospect of efficient generation of multipartite entangled states in large-scale distributed systems with applications in quantum information processing and metrology.

Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: An efficient implementation of GDQM

Abstract This paper studies the dynamics of nonlocal piezo-magnetic nanobeams (PMNBs) embedded in the local/nonlocal ‎viscoelastic medium through the consistent and paradox-free model of the nonlocal theory. Besides, to perform the dynamic analysis, an exact solution and an efficient approach of Generalized Differential Quadrature Method (GDQM) are introduced. Since the size-dependency of the uniform loads is wrongly neglected by the nonlocal elasticity in differential form, the size-dependency of piezo-magnetic load is applied through the two-phase theory. Also, size dependency of the viscoelastic medium is accurately applied and examined through the solutions presented employing the differential two-phase theory and satisfying the constitutive boundary conditions. In this regard, the two-phase resultant equations of motions together with boundary conditions ‎including the constitutive ones related to two-phase ‎PMNB and the two-phase medium are attained. To confirm the credibility and efficiency of the extracted equations as well as presented solution ‎procedures, several analogical studies are accomplished, and it is shown that the results obtained from the differential relations are reliable and consistence with those extracted from the integral nonlocal relations. It is shown that the present approach of the GDQM simplifies the solution procedures of the nonlocal problems and improves the precisions in the cases close to the pure nonlocal state. The presented results emphasize that the size-dependency of viscoelastic medium, external electric, and magnetic loads play significant roles on the vibration ‎characteristics, and therefore it must be considered based on two-phase theory. The available results can be helpful to achieve an excellent design of smart nanobeams embedded in viscoelastic medium.

Attainable and usable coherence in X states over Markovian and non-Markovian channels

The relations between the resource theoretic measures of quantum coherence are rigorously investigated for various Markovian and non-Markovian channels for the two-qubit $X$ states with specific attention to the maximum and minimum attainable coherence and usefulness of these states in performing quantum teleportation in noisy environment. The investigation has revealed that under both dephasing and dissipative type noises the maximally entangled mixed states and Werner states lose their form and usefulness. However, maximally non-local mixed states (MNMSs) lose their identity in dissipative noise only. Thus, MNMSs are established to be useful in teleporting a qubit with fidelity greater than the classical limit in the presence of dephasing noise. MNMSs also remain useful for device independent quantum key distribution in this case as they still violate Bell's inequality. In the presence of noise, coherence measured by relative entropy of coherence is found to fall faster than the same measured using $l_1$ norm of coherence. Further, information back-flow from the environment to the system is observed over non-Markovian channels which leads to revival in coherence. Additionally, sequential interaction of two qubits with the same environment is found to result in correlated noise on both qubits, and coherence is observed to be frozen in this case under dephasing channel. Under the effect of Markovian and non-Markovian dephasing channels studied here, we observed that MNMSs have maximum relative coherence, i.e., they have the maximum amount of $l_1$ norm of coherence among the states with the same amount of relative entropy of coherence. However, this feature is not visible in any $X$ state evolving over dissipative channels.

Multiparty orthogonal product states with minimal genuine nonlocality

Nonlocality without entanglement and its subsequent generalizations offer deep information-theoretic insights and subsequently find several useful applications. The concept of a genuinely nonlocal set of product states emerges as a natural multipartite generalization of this phenomenon. The existence of such sets eventually raises the problem concerning their entanglement-assisted discrimination. Here, we construct examples of genuinely nonlocal product states for an arbitrary number of parties. The strength of genuine nonlocality of these sets can be considered minimal as their perfect discrimination is possible with entangled resources residing in Hilbert spaces having the smallest possible dimensions. Our constructions lead to fully separable measurements that are impossible to implement even if all but one party come together. Furthermore, they also provide the opportunity to compare different multipartite states that otherwise are incomparable under single copy local manipulation.

Nonlocal sets of orthogonal multipartite product states with less members

We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems \(\mathcal {C}^{d}\otimes \mathcal {C}^{d}\otimes \mathcal {C}^{d}~(d\ge 3)\) and \(\mathcal {C}^d\otimes \mathcal {C}^{d+1}\otimes \mathcal {C}^{d+2}~(d\ge 3)\). Then for general tripartite quantum system \(\mathcal {C}^{n_{1}}\otimes \mathcal {C}^{n_{2}}\otimes \mathcal {C}^{n_{3}}\) \((3\le n_{1}\le n_{2}\le n_{3})\), we obtain \(2(n_{2}+n_{3}-1)-n_{1}\) nonlocal orthogonal product states. Finally, we put forward a new construction approach in \(\mathcal {C}^{d_{1}}\otimes \mathcal {C}^{d_{2}}\otimes \cdots \otimes \mathcal {C}^{d_{n}}\) \((d_1,d_2,\cdots d_n\ge 3,\, n>6)\) multipartite systems. Remarkably, our indistinguishable sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing.

Contextuality-based quantum conferencing

Nonlocality inequalities for multi-party systems act as contextuality inequalities for single qudit systems of suitable dimensions (Heywood and Redhead in Found Phys 13(5):481–499, 1983; Abramsky and Brandenburger in New J Phys 13(11):113036, 2011). In this paper, we propose the procedure for adaptation of nonlocality-based quantum conferencing protocols (NQCPs) to contextuality-based QCPs (CQCPs). Unlike the NQCPs, the CQCPs do not involve nonlocal states. As an illustration of the procedure, we present a QCP based on Mermin’s contextuality inequality. As a significant improvement, we propose a QCP based on CHSH contextuality inequality involving only four-dimensional states irrespective of the number of parties sharing the key. The key generation rate of the latter is twice that of the former. Although CQCPs allow for an eavesdropping attack which has no analog in NQCPs, a way out of this attack is demonstrated. Finally, we examine the feasibility of experimental implementation of these protocols with orbital angular momentum states.

A Quantum Dual-Signature Protocol Based on SNOP States without Trusted Participant.

Quantum dual-signature means that two signed quantum messages are combined and expected to be sent to two different recipients. A quantum signature requires the cooperation of two verifiers to complete the whole verification process. As an important quantum signature aspect, the trusted third party is introduced to the current protocols, which affects the practicability of the quantum signature protocols. In this paper, we propose a quantum dual-signature protocol without arbitrator and entanglement for the first time. In the proposed protocol, two independent verifiers are introduced, here they may be dishonest but not collaborate. Furthermore, strongly nonlocal orthogonal product states are used to preserve the protocol security, i.e., no one can deny or forge a valid signature, even though some of them conspired. Compared with existing quantum signature protocols, this protocol does not require a trusted third party and entanglement resources.

Bell Nonlocality Is Not Sufficient for the Security of Standard Device-Independent Quantum Key Distribution Protocols.

Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local projective measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by postprocessing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on any correlation obtained by measuring local projective measurements on certain entangled nonlocal states, namely, on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different reconciliation techniques are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.

High electrical transport performance and ultralow thermal conductivity realized in Ga doped single-layer octagon-square nitrogene

Improving thermoelectric performance of self-powered operation of electronics has been a continuous effort to relieve energy crisis and environmental degradation. In the branches of thermoelectric research, multiscale phonon engineering and proper doping are effective strategies to reduce lattice thermal conductivity and enhance electrical conductivity of bulk materials, respectively, yet great challenge remains in the modulation of transport properties for low-dimensional structures. Here we propose to employ doping of Ga in the single-layer octagon-square nitrogene (OS-N) as an alternative way to increase its thermoelectric efficiency. Our work demonstrates that salient electronic performance can be obtained benefiting from the convergence of valence band as well as non-localized pz orbital state. At the same time, the relatively complexed configuration of doped system shows a much increased impeding of thermal transport, which is about thirty times lower than that of elemental two-dimensional nitrogene monolayer. This pronounced improvement is attributed to the softening of phonon branches, which increase the scattering phase space and structural anharmonicity. Our work illustrates the realization of tailoring electronic and phonon properties in the dimensionality reduced system and provides a road map for potential applying it in fields such as thermal management and thermoelectrics.

Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source

We have experimentally created a robust, ultrabright and phase-stable polarization-entangled state close to maximally entangled Bell-state with %98-fidelity using the type-II spontaneous parametric down-conversion (SPDC) process in periodically-poled KTiOPO4 (PPKTP) collinear crystal inside a Sagnac interferometer (SI). Bell inequality measurement, Freedman's test, as the different versions of CHSH inequality, and also visibility test which all can be seen as the nonlocal realism tests, imply that our created entangled state shows a strong violation from the classical physics or any hidden-variable theory. We have obtained very reliable and very strong Bell violation as S=2.78±0.01 with high brightness VHV=%(99.969±0.003) and VDA=%(96.751±0.002) and very strong violation due to Freedman test as δF=0.01715±0.00001. Furthermore, using the tomographic reconstruction of quantum states together a maximum-likelihood-technique (MLT) as the numerical optimization, we obtain the physical non-negative definite density operator which shows the nonseparability and entanglement of our prepared state. By having the maximum likelihood density operator, we calculate some important entanglement-measures and entanglement entropies. The Sagnac configuration provides bidirectional crystal pumping yields to high-rate entanglement source which is very applicable in quantum communication, sensing and metrology as well as quantum information protocols, and has potential to be used in quantum illumination-based LIDAR and free-space quantum key distribution (QKD).

Characterizing nonlocality of pure symmetric three-qubit states

We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys. Rev. A, 96, 062310 (2017)) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state do not violate the CHSH inequality and hence they are CHSH-local. However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting of two and three distinct spinors (qubits) respectively, can be distinguished based on the strength of violation in the conditional CHSH nonlocality test. Furthermore, we identify six of the 46 classes of tight Bell inequalities in the three-party, two-setting, two-outcome i.e., (3,2,2) scenario (Phys. Rev. A 94, 062121 (2016)). Among the two inequivalent families of three-qubit pure symmetric states, only the states belonging to three distinct spinor class show maximum violations of these six tight Bell inequalities.

The concealment of accelerated information is possible

The possibility of masking an accelerated two-qubit system by using a minimum number of qubits is discussed. It is shown that the information may be masked in either entangled local states or product non-local separable states. We examine that each partition of these states satisfies the masking conditions. Due to the presence of non-local separable partition, one may consider that it is a type of quantum data hiding scheme. The local/non-local information encoded in the masked entangled state is robust against the decoherence of the acceleration process. The possibility of estimating the acceleration parameter via the entangled/separable masked state increases as the initial entanglement value increases. The efficiency of the masking process is examined by quantifying the fidelity of the accelerated state and its subsystems. It is shown that the fidelity of the masked state is maximum at small initial acceleration, while the minimum fidelity is more than 96%.

Locally distinguishing multipartite orthogonal product states with different entanglement resource

Recently, entanglement-assisted state discrimination has attracted much attention. However, most of the relevant results are about the bipartite quantum states and very little is known about the multipartite case. In this paper, considering the nonlocal orthogonal product states constructed by Jiang and Xu [Phys. Rev. A 102, 032211 (2020)], we first present one protocol to locally distinguish a set of orthogonal product states in $$3\otimes 3 \otimes 3$$ by using a $$2\otimes 2$$ maximally entangled state. Then, we generalize the distinguishing method for the class of nonlocal of orthogonal product states in $$\otimes _{j=1}^n{\mathbb {C}}^{d_j}$$ , where $$n\geqslant 3, d_j\geqslant 2, j=1,2,\ldots ,n$$ . Furthermore, for another class of orthogonal product states in $$\otimes _{j=1}^n{\mathbb {C}}^{d_j}$$ , where $$n\geqslant 3, d_j\geqslant 3, j=1,2,\ldots ,n$$ , we prove that these states can also be distinguished by LOCC with a $$3\otimes 3$$ maximally entangled state or two copies of $$2\otimes 2$$ maximally entangled states. The above results can let us better understand how to use entanglement resource more efficiently in multipartite quantum systems and also reveal the phenomenon of less nonlocality with more entanglement.

Room-Temperature Observation of Local and Nonlocal Electronic Quantum States on the Surface of Silicon

Room-Temperature Observation of Local and Nonlocal Electronic Quantum States on the Surface of Silicon

Localization and discrete probability function of Szegedy’s quantum search one-dimensional cycle with self-loops

We study the localization and the discrete probability function of a quantum search on the one-dimensional (1D) cycle with self-loops for n vertices and m marked vertices. First, unmarked vertices have no localization since the quantum search on unmarked vertices behaves like the 1D three-state quantum walk (3QW) and localization does not occur with nonlocal initial states on a 3QW, according to residue calculations and the Riemann-Lebesgue theorem. Second, we show that localization does occur on the marked vertices and derive an analytic expression for localization by the degenerate 1-eigenvalues contributing to marked vertices. Therefore localization can contribute to a quantum search. Furthermore, we emphasize that localization comes from the self-loops. Third, using the localization of a quantum search, the asymptotic average probability distribution (AAPD) and the discrete probability function (DPF) of a quantum search are obtained. The DPF shows that Szegedy’s quantum search on the 1D cycle with self-loops spreads ballistically.