Degree of entanglement for two qutrits in a pure state

Optimal entanglement witnesses for two qutrits

We provide a proof that entanglement witnesses considered recently in [D. Chruściński, F.A. Wudarski, arXiv:1105.4821] are optimal.

Measuring Qutrit-Qutrit Entanglement of Orbital Angular Momentum States of an Atomic Ensemble and a Photon

Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.

Entanglement Teleportation by Qutrits

Quantum entanglement, like othre resources, is now coonsidered to be a resource which can be produced, concentrated if required, transported and consumed. After its inception [1] in 1933, various schemes of quantum state teleportation have been proposed using different types of channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper we investigate the teleportation of an unknown single qutrit state as well as two qutrit state through a three qutrit quantum channel along with the required operations to recover th…

双三能级系统与自旋链耦合的纠缠动力学

Entanglement dynamics of a two-qutrits system coupled to a spin chain

研究双三能级系统与自旋环境耦合的纠缠动力学，利用负性作为纠缠度量，发现快速衰减的纠缠会导致环境发生量子相变。

Inertia of two-qutrit entanglement witnesses

Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertias of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertias of the patial transpose of the two-qutrit bipartite NPT states. As an application, we extend our results to high dimensional states.

Dynamics of entanglement in qubit-qutrit with x component of DM interaction

In this present paper we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii-Moriya $(D_{x})$ by taking an auxiliary qubit C. Here we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction. We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and $D_{x}$ on entanglement. We find that the state (probability amp…

The effect of anisotropy and external magnetic filed on the thermal entanglement in a two-spin-qutrit system

We study the thermal entanglement in a two-spin-qutrit system with anisotropy in the exchange coupling between two spins. We use the realignment criterion to distinguish the entangled states, and the negativity for measuring the entanglement in this system. We see that the anisotropy can provide an additional parameter for enhancing the entanglement.

SU(N)代数与二分量子比特和量子三态系统纠缠的新经验法则

SU(N) algebras and new thumbrules for entanglement of bipartite qubit and qutrit systems

本文基于施密特分解提出检验二分量子比特与量子三态系统纠缠的新经验法则，并揭示其分别由SU(2)和SU(3)代数结构支撑。

Protecting qutrit-qutrit entanglement by weak measurement and reversal

Entangled states in high dimensional systems are of great interest due to the extended possibilities they provide in quantum information processing. Recently, Sun et al. [Phys. Rev. A 82, 052323 (2010)] and Kim et al. [Nat. Phys. 8, 117 (2012)] pointed out that weak measurement and quantum weak measurement reversal can actively combat decoherence. We generalize their studies from qubits to qutrits under amplitude damping decoherence. We find that the qutrit-qutrit entanglement can be partially retrieved for certain initial states when only weak measurement reversals are performed. However, we …

Entanglement witnesses and geometry of entanglement of two--qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert--Schmidt space and investigate the geometry of entanglement. In particular, for a two--parameter family of two--qutrit states that are part of the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three--parameter family of states. In this way we discover new regions of bound entangled states. Furthermore we outline how to use our method to distinguish entangled from separable states.

Evolution Of Entanglement In Groverian Search Algorithm: Two-Qutrit System

Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for entanglement measure defined in terms of success rate of Grover's search algorithm has been obtained for a two-qutrit system and the calculated results agree well with the conventional entropy based measure. Qutrit system are of special interest because the Hilbert space dimensionality (for a given number of qudits-d-dimensional system)is optimal for d=3 and this may be of significance in the enhancement of computing power.

Qutrit Entanglement

We consider the separability of various joint states for N qutrits. We derive two results: (i) the separability condition for a two-qutrit state that is a mixture of the maximally mixed state and a maximally entangled state (such a state is a generalization of the Werner state for two qubits); (ii) upper and lower bounds on the size of the neighborhood of separable states surrounding the maximally mixed state for N qutrits.

Alternative Decomposition of Two-Qutrit Pure States and Its Relation with Entanglement Invariants

Based on maximally entangled states in the full- and sub-spaces of two qutrits, we present an alternative decomposition of two-qutrit pure states in a form $|Ψ>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>) +\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{iθ}|02>$. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter $p_1$ is shown to be an entanglement invariant.

Entanglement certification and quantification in spatial-bin photonic qutrits

Higher dimensional quantum systems are an important avenue for new explorations in quantum computing as well as quantum communications. One of the ubiquitous resources in quantum technologies is entanglement. However, so far, entanglement has been certified in higher dimensional systems through suitable bounds on known entanglement measures. In this work, we have, for the first time, quantified the amount of entanglement in bi-partite pure qutrit states by analytically relating statistical correlation measures and known measures of entanglement, and have determined the amount of entanglement i…

Entanglement of qutrits and ququarts

We investigate in a general form entanglement of biphoton qutrits and ququarts, i.e. states formed in the processes of collinear and, correspondingly, degenerate and non-degenerate Spontaneous Parametric Down-Conversion. Indistinguishability of photons and, for ququarts, joint presence of the frequency and and polarization entanglement are fully taken into account. In the case of qutrits the most general 3-parametric families of maximally entangled and non-entangled states are found, and anti-correlation of the degree of entanglement and polarization is shown to occur and to be characterized b…

Entanglement sudden death in qubit-qutrit systems

We demonstrate the existence of entanglement sudden death (ESD), the complete loss of entanglement in finite time, in qubit-qutrit systems. In particular, ESD is shown to occur in such systems initially prepared in a one-parameter class of entangled mixed states and then subjected to local dephasing noise. Together with previous results, this proves the existence of ESD for some states in all quantum systems for which rigorously defined mixed-state entanglement measures have been identified. We conjecture that ESD exists in all quantum systems prepared in appropriate bipartite states.

Entanglement of simultaneous and non-simultaneous Accelerated Qubit-Qutrit systems

In this contribution, we investigate the entanglement behavior of a composite system consists of two different dimensional subsystems in non-inertial frames. In particular, we consider a composite system of qubit(two-dimensional) subsystem, and qutrit, (three-dimensional) subsystem. The degree of entanglement is quantified for different cases, where it is assumed that the two-subsystems are simultaneously or non- simultaneously accelerated. The entanglement decays as the acceleration of any subsystem increases.In general, the decay rate of entanglement increases as the dimensional of the accel…

Enhancing entanglement, local and non-local information of accelerated two-qubit and two- qutrit systems via weak-reverse measurements

The possibility of recovering and protecting the entanglement of accelerated 2-qubit and 2-qutrit systems is discussed using weak-reverse measurements. The accelerated partial entangled states are more responsive to be protected than the accelerated maximum entangled states. The accelerated coded local information in qutrit system is more robust than that encoded in a 2-qubit system, and it can be conserved even for larger values of accelerations. Meanwhile, the non-accelerated information in qubit system is not affected by the local operation compared with that depicted on qutrit system. For …

Thermal entanglement in a two-qutrit system with nonlinear coupling under nonuniform external magnetic field

We study the thermal entanglement of a 2-qutrit spin chain with nonlinear coupling in the presence of nonuniform magnetic field. Thermal entanglement of an arbitrary (finite dimensional) m-partite system vanishes at some finite threshold temperature T_s. We investigate the dependence of T_s on the system's parameters, i.e. the nonlinear coupling and the magnetic field, for this 2-qutrit system. In addition, we compare two lower bounds of I-concurrence for this system and also study its dense coding capacity as a function of system's parameters.

Dynamics of entanglement for a two-parameter class of states in a qubit-qutrit system

We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death (ESD) is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the case with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in v…

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement, is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature, different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantita…

Protection of entanglement for a two-qutrit V-type open system on the basis of system-reservoir bound states

In this work, a mechanism for long time protection of entanglement of a two-qutrit V-type atomic system each of which interacts independently with a dissipative reservoir is investigated. It is shown that the protection process is related exclusively on the formation of bound states in the system-reservoir energy spectrum. It is demonstrated that the degree of boundedness for the system-reservoir bound states is well-controlled by entering other V-type qutrits into the reservoirs, and also through the manipulation of the spontaneously generated interference related to decay channels of the V-t…

The Entanglement Level and the Detection of Quantum Data Transfer Correctness in Short Qutrit Spin Chains

The quantum entanglement is an important feature of many protocols in the field of quantum computing. In this paper we evaluate a level of entanglement in short qutrit chains. This evaluation is carried out with use of the CCNR criterion and the concurrence measure. We also present some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Utilizing the obtained results, we indicate that analyzing the level of entanglement allows to detect the noise or deviation in the transfer process, in comparison to the perfect transfer where only operat…

Stationary state entanglement and total correlation of two qubits or qutrits

We investigate the mutual information and entanglement of stationary state of two locally driven qubits under the influence of collective dephasing. It is shown that both the mutual information and the entanglement of two qubits in the stationary state exhibit damped oscillation with the scaled action time $γ{T}$ of the local external driving field. It means that we can control both the entanglement and total correlation of the stationary state of two qubits by adjusting the action time of the driving field. We also consider the influence of collective dephasing on entanglement of two qutrits …

The geometry of bipartite qutrits including bound entanglement

We investigate the state space of bipartite qutrits. We construct an analog to the "magic" tetrahedron for bipartite qubits--a magic simplex W. It is formed by all convex combination of nine Bell states which are constructed using the Weyl operators. Due to the high symmetry it is enough to consider certain typical slices through W. Via optimal entanglement witnesses we find regions of bound entangled states inside W.

Two-qutrit Entanglement Witnesses and Gell-Mann Matrices

The Gell-Mann $λ$ matrices for Lie algebra su(3) are the natural basis for the Hilbert space of Hermitian operators acting on the states of a three-level system(qutrit). So the construction of EWs for two-qutrit states by using these matrices may be an interesting problem. In this paper, several two-qutrit EWs are constructed based on the Gell-Mann matrices by using the linear programming (LP) method exactly or approximately. The decomposability and non-decomposability of constructed EWs are also discussed and it is shown that the $λ$-diagonal EWs presented in this paper are all decomposable b…

两量子三能级纠缠的几何与操作特性

Geometric and Operational Characterization of Two-Qutrit Entanglement

本文提出通过几何和操作视角研究两量子三能级纠缠，利用行列式定义不变量并建立与光学干涉仪的对应关系，揭示纠缠态的几何特征和操作属性。

Classification of Bipartite and Tripartite Qutrit Entanglement under SLOCC

We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of biqutrit states and twelve equivalent classes of triqutrit states respectively.

Entanglement dynamics of a qubit-qutrit system in non-inertial frames

The effect of decoherence on a qubit-qutrit system under the influence of global and multilocal decoherence in non-inertial frames is investigated. It is shown that the entanglement sudden death (ESD) can be avoided in non-inertial frames in the presence of dephasing and bit-trit phase flip channels for entire range of decoherence. However, ESD behaviour is seen for higher level of decoherence in case of phase flip and bit-trit flip channels. Irrespective of the entanglement degradation caused by the Unruh effect, no ESD occurs for the dephasing environment. Furthermore, flipping channels have…

The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system

We investigate the effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system by applying the concept of negativity. It is found that the nonlinear couplings favor the thermal entanglement creating. Only when the nonlinear couplings $|K|$ are larger than a certain critical value does the entanglement exist. The dependence of the thermal entanglement in this system on the magnetic field and temperature is also presented. The critical magnetic field increases with the increasing nonlinear couplings constant $|K|$. And for a fixed nonlinear …

Immunity, Improving and Retrieving the lost entanglement of accelerated qubit-qutrit system via local Filtering

The possibility of immunized and improving the entanglement of accelerated systems via local filtering is discussed. The maximum bounds of entanglement depend on the dimensions of the accelerated and the filtered subsystems. If the small dimensional subsystem is accelerated and the large dimensional subsystem is filtered, one can get a long-lived entanglement. Moreover, if the larger subsystem is accelerated, then by filtering any subsystem, the upper bounds of entanglement of the filtered state are larger then that for the initial states.For any accelerated subsystem, the entanglement always …

Quantitative bound entanglement in two-qutrit states

Among the many facets of quantum correlations, bound entanglement has remained one the most enigmatic phenomena, despite the fact that it was discovered in the early days of quantum information. Even its detection has proven to be difficult, let alone its precise quantitative characterization. In this work, we present the exact quantification of entanglement for a two-parameter family of highly symmetric two-qutrit mixed states, which contains a sizable part of bound entangled states. We achieve this by explicitly calculating the convex-roof extensions of the linear entropy as well as the conc…

Generation and sudden death of entanglement in qubit-qutrit systems in depolarizing noise

The dynamics of entanglement in some hybrid qubit-qutrit systems under the influence of global, collective, local and multilocal depolarizing noise is studied. It is shown that the depolarizing noise can be used to induce entanglement. A critical point exists under every coupling of the system with the environment at which all the states are equally entangled. Furthermore, it is seen that no ESD occurs when either only the qubit is coupled to its local environment or the system is coupled to multilocal or global environment. This is an important result for various quantum information processin…

Fast entanglement detection for unknown states of two spatial qutrits

We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigati…

Classification and Quantification of Entangled Bipartite Qutrit Pure States

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

高效率三能级纠缠交换与光子数基

High-rate qutrit entanglement swapping with photon-number-basis

本文提出一种针对三能级量子态的纠缠交换协议，结合光子数编码和额外模式基，提升纠缠生成效率，尤其在光子生成概率有限时表现更优。

Decoherence and entanglement degradation of a qubit-qutrit system in non-inertial frames

We study the effect of decoherence on a qubit-qutrit system under the influence of global, local and multilocal decoherence in non-inertial frames. We show that the entanglement sudden death can be avoided in non-inertial frames in the presence of amplitude damping, depolarizing and phase damping channels. However, degradation of entanglement is seen due to Unruh effect. It is shown that for lower level of decoherence, the depolarizing channel degrades the entanglement more heavily as compared to the amplitude damping and phase damping channels. However, for higher values of decoherence parame…

Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entan…

Manipulating biphotonic qutrits

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement induced non-linearities can be employed to dramatically extend the range of possible transforms on biphotonic qutrits; the three level quantum systems formed by the polarisation of two photons in the same spatio-temporal mode. We fully characterise the biphoton-photon entanglement that underpins our technique, thereby realising the first instance of qubit-qutrit entanglement. We discuss an extension of our t…

Entanglement Universality of TGX States in Qubit-Qutrit Systems

We prove that all states (mixed or pure) of qubit-qutrit ($2\times 3$) systems have entanglement-preserving unitary (EPU) equivalence to a compact subset of true-generalized X (TGX) states called EPU-minimal TGX states which we give explicitly. Thus, for any spectrum-entanglement combination achievable by general states, there exists an EPU-minimal TGX state of the same spectrum and entanglement. We use I-concurrence to measure entanglement and give an explicit formula for it for all $2\times 3$ minimal TGX states (a more general set than EPU-minimal TGX states) whether mixed or pure, yielding…

Separability and entanglement of spin $1$ particle

We define the separability and entanglement notion for particle with spin $s=1$. We consider two cases. In the first the particle is composed of two fermions with $s_1=1/2$ and $s_2=1/2$. In the second case the state is the qutrit state which is not composed system. The notion of negativity and concurrence is defined for the qutrit state. The concurrence and negativity of entangled and separable qutrit states determined by the parameters of the density matrix are explicitly calculated. The maximum entanglement of the qutrit state is observed for maximum values of non diagonal matrix elements o…

退极化噪声在引发纠缠突然死亡中的有效性

Effectiveness of Depolarizing noise in causing sudden death of entanglement

研究证明退极化噪声比广义振幅阻尼噪声更有效地引发双部量子系统纠缠突然死亡，且作用更快。

Two-Qutrit entanglement: 56-years old algorithm challenges machine learning

Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit Bell-diagonal states, i.e., mixture of nine mutually orthogonal maximally entangled states. In this article we apply the Gilbert algorithm to revise previously obtained results for this class. In particular we use ``cartography of entanglement'' to argue that most states left in [Hiesmayr, B. C. {\em Scientific Reports} {\bf 11}, 19739 (2021)] as unknown to …

Effect of two-qutrit entanglement on quantum speed limit time of a bipartite V-type open system

In the present paper, quantum speed limit (QSL) time of a bipartite V-type three-level atomic system under the effect of two-qutrit entanglement is investigated. Each party interacts with own independent reservoir. By considering two local unitarily equivalent Wener states and the Horodecki PPT state, as initial states, the QSL time is evaluated for each of them in the respective entangled regions. It is counterintu-itively observe that the effect of entanglement on the QSL time driven from each of the initial Werner states are completely different when the degree of non-Markovianity is consid…

Entanglement creation and distribution on a graph of exchange-coupled qutrits

We propose a protocol that allows both the creation and distribution of entanglement, resulting in two distant parties (Alice and Bob) conclusively sharing a bipartite Bell State. The system considered is a graph of three-level objects ("qutrits") coupled by SU(3) exchange operators. The protocol begins with a third party (Charlie) encoding two lattice sites in unentangled states, and allowing unitary evolution under time. Alice and Bob perform a projective measurement on their respective qutrits at a given time, and obtain a maximally-entangled Bell state with a certain probablility. We also …

超越正部分转置平方猜想：三量子比特情形

Beyond the Positive Partial Transpose Squared Conjecture: The Qutrit Case

研究超出正部分转置（PPT）设置的映射复合问题，针对三量子比特完全正定映射，证明特定条件下映射复合是纠缠破缺的，确定1-不可蒸馏CP映射锥的性质，还证明特定态在任意选择性测量下不能产生终端纠缠。

Qubit-Qutrit ($2 \otimes 3$) quantum systems: An investigation of some quantum correlations under collective dephasing

We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of {\it time-invariant} entanglement and {\it freezing} dynamics of entanglement for this dimension of Hilbert space. Interestingly, we find that for qubit-qutrit systems both of these peculiar features coexist, that is, we observe not only time-invariant entanglement for certain quantum states but we find also find evidence that many quantum states freeze their …

Invariant Quantum Discord in Qubit-Qutrit Systems under Local Dephasing

We investigate the dynamics of quantum discord and entanglement for a class of mixed qubit-qutrit states assuming that only the qutrit is under the action of a dephasing channel. We demonstrate that even though the entanglement in the qubit-qutrit state disappears in a finite time interval, partial coherence left in the system enables quantum discord to remain invariant throughout the whole time evolution.

二次相位量子态中的纠缠秩对偶性

Exact entanglement trade-offs in qutrit and composite-dimensional stabilizer states

研究二次相位量子态中绝对最大纠缠态的构造与认证，利用加法特征正交性推导出秩-纯度对偶性，给出多项式时间认证准则，并构造了AME(17,10001)态。

两qutrit系统中某些秩为5的对称NPT态的纠缠蒸馏

Entanglement Distillation of some Rank-Five Symmetric NPT States in Two-Qutrit Systems

本研究解决两qutrit系统中一类秩5对称NPT态的1-蒸馏问题，揭示其2-蒸馏的结构障碍，并通过数值研究探索该障碍外的2-蒸馏情况。

Quantum Correlation Dynamics for an Open Multi Qutrit System

We study the correlation dynamics of a system composed of arbitrary numbers of qutrits interacting with a common environment. Initially, the system is assumed to be in a low dimensional subspace of the Hamiltonian called "decoherence-free subspace". Environment induced quantum entanglement and discord is calculated between pair of qutrits of the system as measures of non-classical correlations. Finally the steady state distribution of entanglement and discord is determined with respect to the total number of qutrits of the system.

Entanglement dynamics in finite qudit chain in consistent magnetic field

Based on the Liouville-von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains …

Stationary entanglement and nonlocality of two qubits or qutrits collectively interacting with the thermal environment: The role of Bell singlet state

We investigate the stationary entanglement and stationary nonlocality of two qubits collectively interacting with a common thermal environment. We assume two qubits are initially in Werner state or Werner-like state, and find that thermal environment can make two qubits become stationary nonlocality. The analytical relations among average thermal photon number of the environment, entanglement and nonlocality of two qubits are given in details. It is shown that the fraction of Bell singlet state plays a key role in the phenomenon that the common thermal reservoir can enhance the entanglement of…

Experimental investigation of quantum correlations in a two-qutrit spin system

We report an experimental investigation of quantum correlations in a two-qutrit spin system in a single nitrogen-vacancy center in diamond at room temperatures. Quantum entanglement between two qutrits was observed at room temperature and the existence of non-classical correlations beyond entanglement in the qutrit case has been revealed. Our work demonstrates the potential of the NV centers as the multi-qutrit system to execute quantum information tasks and provides a powerful experimental platform for studying fundamental physics of high-dimensional quantum systems in future.