Local numerical range: a versatile tool in the theory of quantum information (2009)
Gawron, Piotr, Puchała, Zbigniew, Miszczak, Jarosław Adam, Skowronek, Łukasz, Choi, Man-Duen, Zyczkowski, Karol \.
We study operators acting on a composite Hilbert space and investigate their local numerical range, local spectral radius and local $C$--spectral radius. Concrete bounds for the local numerical range...
Man-duen Choi, John A. Holbrook, David W. Kribs, P. Halmos, D. Van Nostr
Abstract. We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the...
The multiplicative domain in quantum error correction (2008)
Choi, Man-Duen, Johnston, Nathaniel, Kribs, David W.
We show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that...
Denote by W (A) the numerical range of a bounded linear operator A. For two oper-ators A and B (which may act on different Hilbert spaces), we study the relation between the inclusion relation W (A)...
1 Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators...
Linear-Algebraic Results Associated with Antiferromagnetic Heisenberg Chains* by (2008)
Man-duen Choi, Jeffrey S. Rosenthal, Peter Rosenthal, Y S (j
y S (j+1)
Numerical Ranges and Dilations (2007)
Denote by W (A) the numerical range of a bounded linear operator A. For two operators A and B (which may act on different Hilbert spaces), we study the relation between the inclusion relation W (A) `...
Linear-Algebraic Results Associated with Antiferromagnetic Heisenberg Chains (2007)
Man-duen Choi, Peter Rosenthal, Peter Rosenthal
. This paper analyses the 3 N \Theta 3 N self-adjoint matrix HN = N \Gamma1 P j=1 S (j) x S (j+1) x + S (j) y S (j+1) y + S (j) z S (j+1) z , the Hamiltonian of a spin-1, one-dimensional, Heisenberg...
Norm bounds for summation of two normal matrices (2007)
A sharp upper bound is obtained for [[A+ iB[[, where A and B are n x n Hermitian ma-trices satisfying a I _ A _ a2I and b I _ B _ bI. Similarly, an optimal bound is obtained /or IIU + VII, where U...
Corners of normal matrices (2007)
Bhatia, Rajendra, Choi, Man-Duen
We study various conditions on matrices $B$ and $C$ under which they can be the off-diagonal blocks of a partitioned normal matrix.
The C*-algebra of symmetric words in two universal unitaries (2006)
Choi, Man-Duen, Latremoliere, Frederic
We compute the K-theory of the C*-algebra of symmetric words in two universal unitaries. This algebra is the fixed point C*-algebra for the order-two automorphism of the full C*-algebra of the free...
C*-crossed-products by an order-two automorphism (2006)
Choi, Man-Duen, Latremoliere, Frederic
We describe the representation theory of C*-crossed-products of a unital C*-algebra A by the cyclic group of order 2. We prove that there are two main types of irreducible representations for the...
Higher-Rank Numerical Ranges of Unitary and Normal Matrices (2006)
Choi, Man-Duen, Holbrook, John A., Kribs, David W., Zyczkowski, Karol
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank...
Crossed-product C*-algebras for conformal automorphisms of the disk (2005)
Choi, Man-Duen, Latremoliere, Frederic
We study the C*-algebra crossed-product of the closed unit disk by the action of one of its conformal automorphisms. After classifying the conformal automorphisms up to topological conjugacy, we...
Higher-Rank Numerical Ranges and Compression Problems (2005)
Choi, Man-Duen, Kribs, David W., Zyczkowski, Karol
We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory...
Quantum Error Correcting Codes From The Compression Formalism (2005)
Choi, Man-Duen, Kribs, David W., Zyczkowski, Karol
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels...
A method to find quantum noiseless subsystems (2005)
Choi, Man-Duen, Kribs, David W.
We develop a structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary (not necessarily unital) quantum operations. The theory can be alternatively phrased in...
Constraint Unitary Dilations and Numerical Ranges (1999)
It is shown that each contraction A on a Hilbert space H, with A + A I for some 2 R, has a unitary dilation U on H \Phi H satisfying U + U I. This is used to settle a conjecture of Halmos in the...