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Show that B,..., B, are also Kraus operators for E. 6. Even though the Kraus representation gives an "internal" view of the dynamics of the open system Q, the Kraus operators contain some information about the environment. Concretely, let E be an evolution map with Kraus operators A,..., An, and p a state of Q. Define numbers Way=Tr(ApA;). (a) Show that if the initial state of E is pure (that is, 10)(0 for some unit vector 10)) and U(Q) is as in question 4, then the matrix (W) is the final density operator of E. (b) Suppose that Q is a qubit and the the Kraus operators for E are al and bZ, where a,beR with a += 1. First confirm that E maps density operators to density operators. Second, find the eigenvalues of the final state of E when the p is one of |0)(0), |+)(+I, and 1.

Show that B,..., B, are also Kraus operators for E. 6. Even though the Kraus representation gives an "internal" view of the dynamics of the open system Q, the Kraus operators contain some information about the environment. Concretely, let E be an evolution map with Kraus operators A,..., An, and p a state of Q. Define numbers Way=Tr(ApA;). (a) Show that if the initial state of E is pure (that is, 10)(0 for some unit vector 10)) and U(Q) is as in question 4, then the matrix (W) is the final density operator of E. (b) Suppose that Q is a qubit and the the Kraus operators for E are al and bZ, where a,beR with a += 1. First confirm that E maps density operators to density operators. Second, find the eigenvalues of the final state of E when the p is one of |0)(0), |+)(+I, and 1.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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No SIM 3:59 PM O 0 74% Yesterday Edit 4:40 PM Show that B,..., B, are also Kraus operators for E. 6. Even though the Kraus representation gives an "internal" view of the dynamics of the open system Q, the Kraus operators contain some information about the environment. Concretely, let E be an evolution map with Kraus operators A1,..., A,, and p a state of Q. Define numbers Wa = Tr(ApA;). (a) Show that if the initial state of E is pure (that is, 10)(0| for some unit vector |0)) and UQE) is as in question 4, then the matrix [Wj is the final density operator of Е. (b) Suppose that Q is a qubit and the the Kraus operators for E are al and bz, where a, b eR with a² + b² = 1. First confirm that E maps density operators to density operators. Second, find the eigenvalues of the final state of E when the p is one of |0)(0), |+)(+|, and 1 2 Add a Caption
Transcribed Image Text:No SIM 3:59 PM O 0 74% Yesterday Edit 4:40 PM Show that B,..., B, are also Kraus operators for E. 6. Even though the Kraus representation gives an "internal" view of the dynamics of the open system Q, the Kraus operators contain some information about the environment. Concretely, let E be an evolution map with Kraus operators A1,..., A,, and p a state of Q. Define numbers Wa = Tr(ApA;). (a) Show that if the initial state of E is pure (that is, 10)(0| for some unit vector |0)) and UQE) is as in question 4, then the matrix [Wj is the final density operator of Е. (b) Suppose that Q is a qubit and the the Kraus operators for E are al and bz, where a, b eR with a² + b² = 1. First confirm that E maps density operators to density operators. Second, find the eigenvalues of the final state of E when the p is one of |0)(0), |+)(+|, and 1 2 Add a Caption
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