Common use of Concluding Remarks Clause in Contracts

Concluding Remarks. We have considered the model of information-theoretic key agreement by public discussion from correlated information. More precisely, we have com- pared scenarios where the joint information is given by classical random variables and by quantum states (e.g., after execution of a quantum pro- tocol). We proved a close connection between such classical and quantum information, namely between intrinsic information and entanglement. As an application, the derived parallels lead to an efficiently verifiable criterion for the fact that the intrinsic information vanishes. Previously, this quantity was considered to be quite hard to handle. Furthermore, we have presented examples providing evidence for the fact that the close connections between classical and quantum information ex- tend to the level of the protocols. As a consequence, the powerful tools and statements on the existence or rather non-existence of quantum-privacy- amplification protocols immediately carry over to the classical scenario, where it is often unclear how to show that no protocol exists. In particular, many examples (only some of which are presented above due to space limi- tations) coming from measuring bound entangled states, and for which none of the known classical secret-key agreement protocols is successful, strongly suggest that bound entanglement has a classical counterpart: intrinsic in- formation which cannot be distilled to a secret key. This stands in sharp contrast to what was previously believed about classical key agreement. We state as an open problem to rigorously prove Conjectures 1 and 2. Finally, we have proposed a measure for entanglement, based on classical information theory, with all the properties required for such a measure. References‌‌‌ [1] X. Xxxxxxxx-Xxxxxxxxxxx and X. Xxxxx, Incoherent and coherent xxxxx- dropping in the six-state protocol of quantum cryptography, Phys. Rev. A, Vol. 59, No. 6, pp. 4238–4248, 1999.

Concluding Remarks. We have considered the model of information-theoretic key agreement by public discussion from correlated information. More precisely, we have com- pared scenarios compared sce- narios where the joint information is given by classical random variables and by quantum states (e.g., after execution of a quantum pro- tocolprotocol). We proved a close connection between such classical and quantum information, namely between intrinsic information and entanglement. As an application, the derived parallels lead to an efficiently verifiable efficiently verifiable criterion for the fact that the intrinsic information vanishes. Previously, this quantity was considered to be quite hard to handle. Furthermore, we have presented examples providing evidence for the fact that the close connections between classical and quantum information ex- tend extend to the level of the protocols. As a consequence, A consequence would be that the powerful tools and statements on the existence or rather non-existence of quantum-privacy- amplification amplification protocols immediately carry over to the classical scenario, where it is often unclear how to show that no protocol exists. In particular, many Many examples (only some of which are presented above due to space limi- tationslimitations) coming from measuring bound entangled states, and for which none of the known classical secret-key agreement protocols is successful, strongly suggest that bound entanglement has a classical counterpart: intrinsic in- formation information which cannot be distilled to a secret key. This stands in sharp contrast to what was previously believed about classical key agreement. We state as an open problem to rigorously prove Conjectures 1 and 2. Finally, we have proposed a measure for entanglement, based on classical information theory, with all the properties required for such a measure. References‌‌‌ [1] X. Xxxxxxxx-Xxxxxxxxxxx and X. Xxxxx, Incoherent and coherent xxxxx- dropping in the six-state protocol of quantum cryptography, Phys. Rev. A, Vol. 59, No. 6, pp. 4238–4248, 1999.

Concluding Remarks. We have considered the model of information-theoretic key agreement by public discussion from correlated information. More precisely, we have com- pared scenarios where the joint information is given by classical random variables and by quantum states (e.g., after execution of a quantum pro- tocol). We proved a close connection between such classical and quantum information, namely between intrinsic information and entanglement. As an application, the derived parallels lead to an efficiently verifiable criterion for the fact that the intrinsic information vanishes. Previously, this quantity was considered to be quite hard to handle. Furthermore, we have presented examples providing evidence for the fact that the close connections between classical and quantum information ex- tend to the level of the protocols. As a consequence, the powerful tools and statements on the existence or rather non-existence of quantum-privacy- amplification protocols immediately carry over to the classical scenario, where it is often unclear how to show that no protocol exists. In particular, many examples (only some of which are presented above due to space limi- tations) coming from measuring bound entangled states, and for which none of the known classical secret-key agreement protocols is successful, strongly suggest that bound entanglement has a classical counterpart: intrinsic in- formation which cannot be distilled to a secret key. This stands in sharp contrast to what was previously believed about classical key agreement. We state as an open problem to rigorously prove Conjectures 1 and 2. Finally, we have proposed a measure for entanglement, based on classical information theory, with all the properties required for such a measure. References‌‌‌ [1] X. Xxxxxxxx-Xxxxxxxxxxx and X. Xxxxx, Incoherent and coherent xxxxx- dropping in the six-state protocol of quantum cryptography, Phys. Rev. A, Vol. 59, No. 6, pp. 4238–4248, 1999.

Concluding Remarks. We have considered the model of information-theoretic key agreement by public discussion from correlated information. More precisely, we have com- pared scenarios compared sce- narios where the joint information is given by classical random variables and by quantum states (e.g., after execution of a quantum pro- tocolprotocol). We proved a close connection between such classical and quantum information, namely between intrinsic information and entanglement. As an application, the derived parallels lead to an efficiently verifiable e ciently veri able criterion for the fact that the intrinsic information vanishes. Previously, this quantity was considered to be quite hard to handle. Furthermore, we have presented examples providing evidence for the fact that the close connections between classical and quantum information ex- tend extend to the level of the protocols. As a consequence, A consequence would be that the powerful tools and statements on the existence or rather non-existence of quantum-privacy- amplification ampli cation protocols immediately carry over to the classical scenario, where it is often unclear how to show that no protocol exists. In particular, many Many examples (only some of which are presented above due to space limi- tationslimitations) coming from measuring bound entangled states, and for which none of the known classical secret-key agreement protocols is successful, strongly suggest that bound entanglement has a classical counterpart: intrinsic in- formation information which cannot be distilled to a secret key. This stands in sharp contrast to what was previously believed about classical key agreement. We state as an open problem to rigorously prove Conjectures 1 and 2. Finally, we have proposed a measure for entanglement, based on classical information theory, with all the properties required for such a measure. References‌‌‌ [1] X. Xxxxxxxx-Xxxxxxxxxxx and X. Xxxxx, Incoherent and coherent xxxxx- dropping in the six-state protocol of quantum cryptography, Phys. Rev. A, Vol. 59, No. 6, pp. 4238–4248, 1999.

Concluding Remarks. We have considered the model of information-theoretic key agreement by public discussion from correlated information. More precisely, we have com- pared scenarios compared sce- narios where the joint information is given by classical random variables and by quantum states (e.g., after execution of a quantum pro- tocolprotocol). We proved a close connection between such classical and quantum information, namely between intrinsic information and entanglement. As an application, the derived parallels lead to an efficiently verifiable criterion for the fact that the intrinsic information vanishes. Previously, this quantity was considered to be quite hard to handle. Furthermore, we have presented examples providing evidence for the fact that the close connections between classical and quantum information ex- tend extend to the level of the protocols. As a consequence, A consequence would be that the powerful tools and statements on the existence or rather non-existence of quantum-privacy- amplification protocols immediately carry over to the classical scenario, where it is often unclear how to show that no protocol exists. In particular, many Many examples (only some of which are presented above due to space limi- tationslimitations) coming from measuring bound entangled states, and for which none of the known classical secret-key agreement protocols is successful, strongly suggest that bound entanglement has a classical counterpart: intrinsic in- formation information which cannot be distilled to a secret key. This stands in sharp contrast to what was previously believed about classical key agreement. We state as an open problem to rigorously prove Conjectures 1 and 2. Finally, we have proposed a measure for entanglement, based on classical information theory, with all the properties required for such a measure. References‌‌‌ [1] X. Xxxxxxxx-Xxxxxxxxxxx and X. Xxxxx, Incoherent and coherent xxxxx- dropping in the six-state protocol of quantum cryptography, Phys. Rev. A, Vol. 59, No. 6, pp. 4238–4248, 1999.