Two and three-uniform states from irredundant orthogonal arrays
| Autor: | Shan-Qi Pang, Xiao Zhang, Xiao Lin, Qingjuan Zhang |
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| Rok vydání: | 2019 |
| Předmět: |
Discrete mathematics
Class (set theory) Series (mathematics) Computer Networks and Communications Statistical and Nonlinear Physics Quantum Physics 01 natural sciences lcsh:QC1-999 lcsh:QA75.5-76.95 010305 fluids & plasmas Computational Theory and Mathematics Quantum state Qubit 0103 physical sciences Computer Science (miscellaneous) lcsh:Electronic computers. Computer science Orthogonal array Quantum information 010306 general physics Prime power Hamming code lcsh:Physics Mathematics |
| Zdroj: | npj Quantum Information, Vol 5, Iss 1, Pp 1-10 (2019) |
| ISSN: | 2056-6387 |
| DOI: | 10.1038/s41534-019-0165-8 |
| Popis: | 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 2-uniform 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 3-uniform states are obtained from IrOA(32, 10, 2, 3) and IrOA(32, 11, 2, 3) using the interaction column property of OAs. |
| Databáze: | OpenAIRE |
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