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A matrix convexity approach to some celebrated quantum inequalities
 Proc. Nat. Acad. Sci. USA
"... Dedicated to Gert Pedersen, who is missed for both his brilliance and his exuberant sense of humor. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequalities. A general argument is given using matrix p ..."
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Cited by 26 (2 self)
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Dedicated to Gert Pedersen, who is missed for both his brilliance and his exuberant sense of humor. Abstract. Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the HansenPedersenJensen inequalities. A general argument is given using matrix perspectives of operator convex functions. A matrix analogue of Maréchal’s extended perspectives provides additional inequalities, including a p + q ≤ 1 result of Lieb. 1.
A Minkowski type trace inequality and strong subadditivity of quantum entropy
 Advances in the Mathematical Sciences, AMS Transl., 189 Series 2
, 1999
"... We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is ..."
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Cited by 25 (4 self)
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We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is
Semidefinite programs for completely bounded norms
, 2009
"... The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them. ..."
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Cited by 20 (3 self)
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The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them.
Random quantum circuits are approximate 2designs
, 2008
"... Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approxima ..."
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Cited by 14 (3 self)
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Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haardistributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1 and 2designs. Previous constructions required longer circuits and worked only for specific gate sets. As a corollary of our main result, we also improve previous bounds on the convergence rate of random walks on the Clifford group. 1
Computing stabilized norms for quantum operations via the theory of completely bounded maps
"... Abstract. The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of completely bounded maps, we formulate an algorithm t ..."
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Cited by 6 (0 self)
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Abstract. The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of completely bounded maps, we formulate an algorithm to compute the norm of an arbitrary linear map. We present an implementation of the algorithm via Maple, discuss its efficiency, and consider the case of differences of unitary maps. 1.
Strong converse exponents for a quantum channel discrimination problem and quantumfeedbackassisted communication
, 2014
"... quantumfeedbackassisted communication ..."
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Comparison of matrix norms on bipartite spaces
, 2009
"... Two noncommutative versions of the classical L q (L p) norm on the product matrix algebras Mn ⊗ Mm are compared. The first norm was defined recently by Carlen and Lieb, as a byproduct of their analysis of certain convex functions on matrix spaces. The second norm was defined by Pisier and others us ..."
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Cited by 2 (0 self)
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Two noncommutative versions of the classical L q (L p) norm on the product matrix algebras Mn ⊗ Mm are compared. The first norm was defined recently by Carlen and Lieb, as a byproduct of their analysis of certain convex functions on matrix spaces. The second norm was defined by Pisier and others using results from the theory of operator spaces. It is shown that the second norm is upper bounded by a constant multiple of the first for all 1 ≤ p ≤ 2, q ≥ 1. In one case (2 = p < q) it is also shown that there is no such lower bound, and hence that the norms are inequivalent. It is conjectured that the norms are inequivalent in all cases. 1