{"title":"实现调整操作实验的理论建议","authors":"Shruti Aggarwal, Satyabrata Adhikari","doi":"10.1007/s11128-024-04422-w","DOIUrl":null,"url":null,"abstract":"<p>Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment operation is not known yet. In this paper, we address the problem of experimental realization of realignment operation, and to achieve this aim, we propose a theoretical proposal for the same. We first show that after applying the realignment operation on a bipartite state, the resulting matrix can be expressed in terms of the partial transposition operation along with column interchange operations. We observed that these column interchange operations forms a permutation matrix which can be implemented via SWAP operator acting on the density matrix. This mathematical framework is used to exactly determine the first moment of the realignment matrix experimentally. This has been done by showing that the first moment of the realignment matrix can be expressed as the expectation value of a SWAP operator which indicates the possibility of its measurement. Further, we have provided an estimation of the higher-order realigned moments in terms of the first realigned moment and thus pave a way to estimate the higher-order moments experimentally. Next, we develop moment-based entanglement detection criteria that detect positive partial transpose entangled states as well as negative partial transpose entangled states. Moreover, we define a new matrix realignment operation for three-qubit states and have devised an entanglement criteria that is able to detect three-qubit fully entangled states. We have developed various methods and techniques in the detection of bipartite and tripartite entangled states that may be realized in the current technology.</p>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Theoretical proposal for the experimental realization of realignment operation\",\"authors\":\"Shruti Aggarwal, Satyabrata Adhikari\",\"doi\":\"10.1007/s11128-024-04422-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment operation is not known yet. In this paper, we address the problem of experimental realization of realignment operation, and to achieve this aim, we propose a theoretical proposal for the same. We first show that after applying the realignment operation on a bipartite state, the resulting matrix can be expressed in terms of the partial transposition operation along with column interchange operations. We observed that these column interchange operations forms a permutation matrix which can be implemented via SWAP operator acting on the density matrix. This mathematical framework is used to exactly determine the first moment of the realignment matrix experimentally. This has been done by showing that the first moment of the realignment matrix can be expressed as the expectation value of a SWAP operator which indicates the possibility of its measurement. Further, we have provided an estimation of the higher-order realigned moments in terms of the first realigned moment and thus pave a way to estimate the higher-order moments experimentally. Next, we develop moment-based entanglement detection criteria that detect positive partial transpose entangled states as well as negative partial transpose entangled states. Moreover, we define a new matrix realignment operation for three-qubit states and have devised an entanglement criteria that is able to detect three-qubit fully entangled states. We have developed various methods and techniques in the detection of bipartite and tripartite entangled states that may be realized in the current technology.</p>\",\"PeriodicalId\":746,\"journal\":{\"name\":\"Quantum Information Processing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Information Processing\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s11128-024-04422-w\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s11128-024-04422-w","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Theoretical proposal for the experimental realization of realignment operation
Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment operation is not known yet. In this paper, we address the problem of experimental realization of realignment operation, and to achieve this aim, we propose a theoretical proposal for the same. We first show that after applying the realignment operation on a bipartite state, the resulting matrix can be expressed in terms of the partial transposition operation along with column interchange operations. We observed that these column interchange operations forms a permutation matrix which can be implemented via SWAP operator acting on the density matrix. This mathematical framework is used to exactly determine the first moment of the realignment matrix experimentally. This has been done by showing that the first moment of the realignment matrix can be expressed as the expectation value of a SWAP operator which indicates the possibility of its measurement. Further, we have provided an estimation of the higher-order realigned moments in terms of the first realigned moment and thus pave a way to estimate the higher-order moments experimentally. Next, we develop moment-based entanglement detection criteria that detect positive partial transpose entangled states as well as negative partial transpose entangled states. Moreover, we define a new matrix realignment operation for three-qubit states and have devised an entanglement criteria that is able to detect three-qubit fully entangled states. We have developed various methods and techniques in the detection of bipartite and tripartite entangled states that may be realized in the current technology.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.