Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States. Chitambar, E., Miller, C., A., & Shi, Y. Quantum Information and Computation, 11:0813-0819, 2011.
Paper
Website doi abstract bibtex 1 download In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.
@article{
title = {Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States},
type = {article},
year = {2011},
pages = {0813-0819},
volume = {11},
websites = {http://arxiv.org/abs/1010.1018},
id = {9da548cf-e66b-3dca-bb6c-35ad1961d52e},
created = {2019-12-02T15:18:41.624Z},
file_attached = {true},
profile_id = {5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06},
last_modified = {2019-12-02T15:19:18.144Z},
read = {false},
starred = {false},
authored = {true},
confirmed = {true},
hidden = {false},
private_publication = {false},
abstract = {In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.},
bibtype = {article},
author = {Chitambar, Eric and Miller, Carl A. and Shi, Yaoyun},
doi = {10.26421/QIC11.9-10},
journal = {Quantum Information and Computation}
}
Downloads: 1
{"_id":"mDmtvsdzbJeGKTHCB","bibbaseid":"chitambar-miller-shi-decidingunitaryequivalencebetweenmatrixpolynomialsandsetsofbipartitequantumstates-2011","authorIDs":["5de52bdacfb25fde010000b9","5def32aae83f7dde010000e7","5df1168a092ae5df010001eb","5df30153bc9e6cde01000063","5df41026d1756cdf01000190","5df4613eb126eade010000ec","5df8cc40877972de0100001c","5dfb7c63c2820bdf010000da","5e039f61745356de0100007e","5e052da4709177de01000152","5e0bcc1894c532f301000120","5e0ff9cc86fd12e801000004","5e1399ee0d0b99de0100000a","5e1f7fb008195af301000095","5e29d108888177df0100007a","5e2d6c99556d50df01000014","5e31ad636be690de010001d4","5e38625dccda85de010004bd","5e40db72614963de0100019e","5e44b7e67759a7df01000017","5e4571c949667cde0100017c","5e520228bba759e80100000a","5e530e0f6d68b8df010000c0","5e54693f88d190df0100016f","5e56730fdf3460df010000d5","5e5eddfbcc2eefde01000019","5e6079679119f0de010000d7","5e667fa4152d6bde01000163","5gLwgyNbpAEqARny9","HDvX6QCMGCXJq7qfC","PqnfcCTDh2C7T9Fs7","SjW6sDcnoPpgkrpdM","W7YG7gy5PpzLKPAwc","XQwubrYRsLJ7iGbRi","h7zdz6e3hSdGiNbGz","no76tmEdThshKt6Qr","o2ejS6RYLpGPuopad","pombtjmJLe3eqeuMN"],"author_short":["Chitambar, E.","Miller, C., A.","Shi, Y."],"bibdata":{"title":"Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States","type":"article","year":"2011","pages":"0813-0819","volume":"11","websites":"http://arxiv.org/abs/1010.1018","id":"9da548cf-e66b-3dca-bb6c-35ad1961d52e","created":"2019-12-02T15:18:41.624Z","file_attached":"true","profile_id":"5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06","last_modified":"2019-12-02T15:19:18.144Z","read":false,"starred":false,"authored":"true","confirmed":"true","hidden":false,"private_publication":false,"abstract":"In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\\dagger=B_i$ for $0\\leq i\\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.","bibtype":"article","author":"Chitambar, Eric and Miller, Carl A. and Shi, Yaoyun","doi":"10.26421/QIC11.9-10","journal":"Quantum Information and Computation","bibtex":"@article{\n title = {Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States},\n type = {article},\n year = {2011},\n pages = {0813-0819},\n volume = {11},\n websites = {http://arxiv.org/abs/1010.1018},\n id = {9da548cf-e66b-3dca-bb6c-35ad1961d52e},\n created = {2019-12-02T15:18:41.624Z},\n file_attached = {true},\n profile_id = {5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06},\n last_modified = {2019-12-02T15:19:18.144Z},\n read = {false},\n starred = {false},\n authored = {true},\n confirmed = {true},\n hidden = {false},\n private_publication = {false},\n abstract = {In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\\dagger=B_i$ for $0\\leq i\\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.},\n bibtype = {article},\n author = {Chitambar, Eric and Miller, Carl A. and Shi, Yaoyun},\n doi = {10.26421/QIC11.9-10},\n journal = {Quantum Information and Computation}\n}","author_short":["Chitambar, E.","Miller, C., A.","Shi, Y."],"urls":{"Paper":"https://bibbase.org/service/mendeley/5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06/file/7143e147-9b98-17eb-0cb8-415cb852efb6/Chitambar_Miller_Shi___2011___Deciding_Unitary_Equivalence_Between_Matrix_Polynomials_and_Sets_of_Bipartite_Quantum_Stat.pdf.pdf","Website":"http://arxiv.org/abs/1010.1018"},"biburl":"https://bibbase.org/service/mendeley/5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06","bibbaseid":"chitambar-miller-shi-decidingunitaryequivalencebetweenmatrixpolynomialsandsetsofbipartitequantumstates-2011","role":"author","metadata":{"authorlinks":{"chitambar, e":"https://quantum-entangled.ece.illinois.edu/publications/"}},"downloads":1},"bibtype":"article","creationDate":"2019-12-02T15:20:58.207Z","downloads":1,"keywords":[],"search_terms":["deciding","unitary","equivalence","between","matrix","polynomials","sets","bipartite","quantum","states","chitambar","miller","shi"],"title":"Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States","year":2011,"biburl":"https://bibbase.org/service/mendeley/5ed10b2c-e6b8-3ad8-bec0-45bb1010ca06","dataSources":["9eser9nRTJ8sJHJ3r","ya2CyA73rpZseyrZ8","2252seNhipfTmjEBQ"]}