Multipartite entanglement in heterogeneous systems

Goyeneche, Dardo; Bielawski, Jakub; Życzkowski, Karol

doi:10.1103/physreva.94.012346

Cited by 47 publications

(70 citation statements)

References 49 publications

(86 reference statements)

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“…The results presented in this paper will establish a foundation for solving other open problems, such as the construction of k-uniform states of N qudits (d ≥ 2) for k ≥ 4, including the problem stated by Huber et al, 14 and heterogeneous multipartite systems, 17 since the proposed construction methods can be suitable for IrOAs of any strength k ≥ 4 and irredundant mixed orthogonal arrays (IrMOAs). 17,32,33 In the construction process, we often encounter the problem that some uniform states could have fewer terms or qudits. If the Hadamard conjecture is considered, Theorems 2.9 and 2.10 state that the number of terms in many 2-uniform states could be reduced.…”

Section: Discussionmentioning

confidence: 99%

“…There has also been some progress in the construction and characterization of k-uniform states. 1,2,11,[13][14][15][16][17][18] For example, Goyeneche et al 2 constructed a 3-uniform state of six qubits and a 2uniform state of five qubits by the judicial insertion of some minus signs. The nonexistence of the 3-uniform states of seven qubits is proved in.…”

Section: Introductionmentioning

confidence: 99%

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Two and three-uniform states from irredundant orthogonal arrays

et al. 2019

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A pure quantum state of N subsystems, each with d levels, is said to be k-uniform if all of its reductions to k qudits are maximally mixed. Only the uniform states obtained from orthogonal arrays (OAs) are considered throughout this work. The Hamming distances of OAs are specially applied to the theory of quantum information. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant orthogonal arrays (IrOAs), then answer the open questions of whether there exist 3-uniform states of N qubits and 2-uniform states of N qutrits, and whether 3-uniform states of qudits (d > 2) for high values of N can be explicitly constructed. In fact, we obtain 3-uniform states for an arbitrary number of N ≥ 8 qubits and 2uniform states of N qutrits for every N ≥ 4. Additionally, we provide explicit constructions of the 3-uniform states of N ≥ 8 qutrits, N = 6 and N ≥ 8 ququarts and ququints, N ≥ 6 qudits having d levels for any prime power d > 6, and N = 8 and N ≥ 12 qudits having d levels for non-prime-power d ≥ 6. Moreover, we describe an explicit construction scheme for the 2-uniform states of qudits having d ≥ 4 levels. The proofs of existence of the 2-uniform states of N ≥ 6 qubits are simplified by using a class of OAs. Two special 3uniform states are obtained from IrOA(32, 10, 2, 3) and IrOA(32, 11, 2, 3) using the interaction column property of OAs.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two and three-uniform states from irredundant orthogonal arrays

et al. 2019

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“…The only known violations of local realism are weaker than those for two-dimensional systems [114][115][116][117]. In systems where both the number of photons as well as the number of dimensions is larger than two, asymmetric types of entanglement can exist [112,131,132]. There, the connection to violation of local realism and its applications in novel quantum protocols has not been investigated until now.…”

Section: E Stronger Violations Of Quantum Mechanical Vs Local Realimentioning

confidence: 99%

Twisted photons: new quantum perspectives in high dimensions

et al. 2017

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Twisted photons can be used as alphabets to encode information beyond one bit per single photon. This ability offers great potential for quantum information tasks, as well as for the investigation of fundamental questions. In this review article, we give a brief overview of the theoretical differences between qubits and higher dimensional systems, qudits, in different quantum information scenarios. We then describe recent experimental developments in this field over the past three years. Finally, we summarize some important experimental and theoretical questions that might be beneficial to understand better in the near future.

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“…To conclude this section, we remark that the combinatorial techniques presented in this work are not restricted to N -qudit systems. That is, they can also be applied to heterogeneous systems [34], made up of subsystems with a different number of internal levels. We have computed the Hilbert basis for the families (i) OA (2 2 3 1 , k) and (i) OA (2 1 3 2 , k), with k = 1, 2.…”

Section: Five Qubits and Beyondmentioning

confidence: 99%

Coarse-grained entanglement classification through orthogonal arrays

Seveso

Goyeneche

Życzkowski

2018

Journal of Mathematical Physics

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Classification of entanglement in multipartite quantum systems is an open problemsolved so far only for bipartite systems and for systems composed of three and four qubits. We propose here a coarse-grained classification of entanglement in systems consisting of N subsystems with an arbitrary number of internal levels each, based on properties of orthogonal arrays with N columns. In particular, we investigate in detail a subset of highly entangled pure states which contains all states defining maximum distance separable codes. To illustrate the methods presented, we analyze systems of four and five qubits, as well as heterogeneous tripartite systems consisting of two qubits and one qutrit or one qubit and two qutrits. I. INTRODUCTIONCharacterization of entanglement in multipartite systems has proven particularly challenging, even for pure states. As one moves from a bipartite to a multipartite scenario involving N parties, the algebraic structure becomes much richer. A pure multipartite quantum state is de-arXiv:1709.05916v4 [math.CO] 28 Jun 2018 := max I:|I|=t J t (I), where |I| denotes the cardinality of the multi-index I. Then, the generalized resolution is defined as(2) Clearly, t < GR < t+1. For two-level OAs, the above quantity is invariant under isomorphisms.However, for multi-level arrays, permutations of symbols within columns can change quantity 2) [23]. Hence the generalized resolution of a multi-level OA is defined as the maximum value of (2) taken over the family of all isomorphic arrays.

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Multipartite entanglement in heterogeneous systems

Cited by 47 publications

References 49 publications

Two and three-uniform states from irredundant orthogonal arrays

Two and three-uniform states from irredundant orthogonal arrays

Twisted photons: new quantum perspectives in high dimensions

Coarse-grained entanglement classification through orthogonal arrays

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