{"title":"通过纯全局噪声环境生成最大纠缠态","authors":"Fan-Zhen Kong, Jun-Long Zhao","doi":"10.1088/1612-202x/ad3627","DOIUrl":null,"url":null,"abstract":"We studied the entangling power of two pure global noises, i.e. amplitude damping noise and classic noise. The entangling power of the two-qubit amplitude damping global noise periodically oscillates with time. Additionally, the entangling power of two-qubit global classical noise increases exponentially with time. The maximum entangling power of both of them exceeds that of the perfect entanglers. Based on this, we propose the conditions for generating a maximally entangled state with global noise acting on a two-qubit separable state. Only if the two-qubit composite system, which is initially in one of those product states: <inline-formula>\n<tex-math><?CDATA $\\frac{1}{\\sqrt{2}}(|0\\rangle \\pm |1\\rangle)\\otimes \\frac{1}{\\sqrt{2}}(|0\\rangle \\pm |1\\rangle)$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mfrac><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>0</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mo>±</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mo stretchy=\"false\">)</mml:mo><mml:mo>⊗</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mfrac><mml:mo stretchy=\"false\">(</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>0</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mo>±</mml:mo><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>, <inline-formula>\n<tex-math><?CDATA $|10\\rangle$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>10</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and <inline-formula>\n<tex-math><?CDATA $|01\\rangle$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo><mml:mn>01</mml:mn><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> suffers an amplitude damping global noise, can we prepare this system in the maximally entangled state by appropriately controlling the evolution time of amplitude damping. Finally, we investigate the disentanglement of the maximum entangled Bell state using these two types of global noise. The two global noises cannot completely disentangle the Bell states <inline-formula>\n<tex-math><?CDATA $\\Phi^{\\pm}$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Φ</mml:mi><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. Under the influence of amplitude damping global noise, the entanglement of Bell state <inline-formula>\n<tex-math><?CDATA $\\Psi^+$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> undergoes a cyclical variation, alternating between disappearance and recovery to reach maximum entanglement within one period. The entanglement of either Bell state <inline-formula>\n<tex-math><?CDATA $\\Psi^+$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn6.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> or <inline-formula>\n<tex-math><?CDATA $\\Psi^-$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn7.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> is completely independent of global classical noise. The entanglement of Bell state <inline-formula>\n<tex-math><?CDATA $\\Psi^-$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi mathvariant=\"normal\">Ψ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"lplad3627ieqn8.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> is also robust against amplitude damping global noise.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generating a maximally entangled state via a pure global noise environment\",\"authors\":\"Fan-Zhen Kong, Jun-Long Zhao\",\"doi\":\"10.1088/1612-202x/ad3627\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We studied the entangling power of two pure global noises, i.e. amplitude damping noise and classic noise. The entangling power of the two-qubit amplitude damping global noise periodically oscillates with time. Additionally, the entangling power of two-qubit global classical noise increases exponentially with time. The maximum entangling power of both of them exceeds that of the perfect entanglers. Based on this, we propose the conditions for generating a maximally entangled state with global noise acting on a two-qubit separable state. Only if the two-qubit composite system, which is initially in one of those product states: <inline-formula>\\n<tex-math><?CDATA $\\\\frac{1}{\\\\sqrt{2}}(|0\\\\rangle \\\\pm |1\\\\rangle)\\\\otimes \\\\frac{1}{\\\\sqrt{2}}(|0\\\\rangle \\\\pm |1\\\\rangle)$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mfrac><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo></mml:mrow><mml:mn>0</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo><mml:mo>±</mml:mo><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mo>⊗</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msqrt><mml:mn>2</mml:mn></mml:msqrt></mml:mfrac><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo></mml:mrow><mml:mn>0</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo><mml:mo>±</mml:mo><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo></mml:mrow><mml:mn>1</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>, <inline-formula>\\n<tex-math><?CDATA $|10\\\\rangle$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo><mml:mn>10</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn2.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and <inline-formula>\\n<tex-math><?CDATA $|01\\\\rangle$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mo stretchy=\\\"false\\\">|</mml:mo><mml:mn>01</mml:mn><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⟩</mml:mo></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn3.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> suffers an amplitude damping global noise, can we prepare this system in the maximally entangled state by appropriately controlling the evolution time of amplitude damping. Finally, we investigate the disentanglement of the maximum entangled Bell state using these two types of global noise. The two global noises cannot completely disentangle the Bell states <inline-formula>\\n<tex-math><?CDATA $\\\\Phi^{\\\\pm}$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mi mathvariant=\\\"normal\\\">Φ</mml:mi><mml:mrow><mml:mo>±</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn4.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. Under the influence of amplitude damping global noise, the entanglement of Bell state <inline-formula>\\n<tex-math><?CDATA $\\\\Psi^+$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mi mathvariant=\\\"normal\\\">Ψ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn5.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> undergoes a cyclical variation, alternating between disappearance and recovery to reach maximum entanglement within one period. The entanglement of either Bell state <inline-formula>\\n<tex-math><?CDATA $\\\\Psi^+$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mi mathvariant=\\\"normal\\\">Ψ</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn6.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> or <inline-formula>\\n<tex-math><?CDATA $\\\\Psi^-$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mi mathvariant=\\\"normal\\\">Ψ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn7.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> is completely independent of global classical noise. The entanglement of Bell state <inline-formula>\\n<tex-math><?CDATA $\\\\Psi^-$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:msup><mml:mi mathvariant=\\\"normal\\\">Ψ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"lplad3627ieqn8.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> is also robust against amplitude damping global noise.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1612-202x/ad3627\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1612-202x/ad3627","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Generating a maximally entangled state via a pure global noise environment
We studied the entangling power of two pure global noises, i.e. amplitude damping noise and classic noise. The entangling power of the two-qubit amplitude damping global noise periodically oscillates with time. Additionally, the entangling power of two-qubit global classical noise increases exponentially with time. The maximum entangling power of both of them exceeds that of the perfect entanglers. Based on this, we propose the conditions for generating a maximally entangled state with global noise acting on a two-qubit separable state. Only if the two-qubit composite system, which is initially in one of those product states: 12(|0⟩±|1⟩)⊗12(|0⟩±|1⟩), |10⟩ and |01⟩ suffers an amplitude damping global noise, can we prepare this system in the maximally entangled state by appropriately controlling the evolution time of amplitude damping. Finally, we investigate the disentanglement of the maximum entangled Bell state using these two types of global noise. The two global noises cannot completely disentangle the Bell states Φ±. Under the influence of amplitude damping global noise, the entanglement of Bell state Ψ+ undergoes a cyclical variation, alternating between disappearance and recovery to reach maximum entanglement within one period. The entanglement of either Bell state Ψ+ or Ψ− is completely independent of global classical noise. The entanglement of Bell state Ψ− is also robust against amplitude damping global noise.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.