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Theory of Quantum Information with Memory [Kõva köide]

  • Formaat: Hardback, 502 pages, kõrgus x laius: 240x170 mm, kaal: 963 g
  • Ilmumisaeg: 22-Aug-2022
  • Kirjastus: De Gruyter
  • ISBN-10: 3110787997
  • ISBN-13: 9783110787993
Teised raamatud teemal:
Theory of Quantum Information with MemorySuurem pilt
  • Formaat: Hardback, 502 pages, kõrgus x laius: 240x170 mm, kaal: 963 g
  • Ilmumisaeg: 22-Aug-2022
  • Kirjastus: De Gruyter
  • ISBN-10: 3110787997
  • ISBN-13: 9783110787993
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783110787993.html
Märksõnad:
There are many books on the theory of quantum information, says Chang, but this is the first to consider infinite dimensionality and memory effects in quantum communication. It covers the formulation of quantum systems, probability measures and convex functions on S(H), completely positive maps, quantum channels and operations, approximation and convergence of quantum channels, von Newmann entropy, relative and conditional entropies, channel output entropies, quantum entanglement, quantum mutual and coherent information, HolevoX-capacity, classical capacities of memoryless channels, the structure of quantum memory channels, channels with Markovian memory, and channels with long-term memory. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)

This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infi nite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.

Preface v
Introduction vii
1 Basic notation and preliminaries
1(32)
1.1 Complex Hilbert and Banach spaces
1(6)
1.2 Linear operators and their adjoints
7(6)
1.2.1 Adjoint and self-adjoint operators
8(1)
1.2.2 Bounded linear operators
9(4)
1.3 Positive operators
13(2)
1.4 Resolvent set and spectrum
15(1)
1.5 Unitary operators
16(1)
1.6 Projection operators
17(4)
1.7 Finite rank and compact linear operators
21(4)
1.7.1 Finite rank linear operators
21(1)
1.7.2 Compact linear operators
22(3)
1.8 Trace-class and Hilbert-Schmidt operators
25(8)
1.8.1 Trace-class operators
25(4)
1.8.2 Hilbert-Schmidt operator
29(4)
2 Formulation of quantum systems
33(38)
2.1 Operator topologies
34(2)
2.2 Operator algebras
36(6)
2.2.1 C*-algebras
37(2)
2.2.2 Von Neumann algebras
39(3)
2.3 Bounded linear functionals
42(11)
2.3.1 Bounded linear functionals on H
44(4)
2.3.2 4* and 4
48(5)
2.4 Quantum states
53(3)
2.5 GNS representation
56(2)
2.6 Quantum observables and measurements
58(4)
2.6.1 Positive operator valued measures
58(1)
2.6.2 Quantum observables
59(1)
2.6.3 Quantum measurements
60(2)
2.7 Tensor products and direct sums
62(5)
2.7.1 Tensor products of Hilbert spaces and operators
62(3)
2.7.2 Direct sum of Hilbert spaces and operators
65(2)
2.8 Composite quantum systems
67(4)
2.8.1 Composite system as tensor products
67(1)
2.8.2 Partial Traces
67(4)
3 Probability measures and convex functions on 5(H)
71(24)
3.1 Probability measures on 5(H)
71(3)
3.1.1 Support of Borel measures
71(3)
3.2 Some compactness criteria
74(6)
3.2.1 Compactness criteria on 5(H)
74(5)
3.2.2 Compactness criteria on P(5(H))
79(1)
3.3 Barycenters
80(8)
3.3.1 A brief review of convex analysis
80(1)
3.3.2 Properties of barycenter
81(7)
3.4 Convex functions on S(H)
88(7)
3.4.1 σ-convexity and μ-convexity
88(3)
3.4.2 Convex hull and convex closure
91(4)
4 Com pletely positive maps
95(22)
4.1 Definitions and properties
95(7)
4.2 Some technical results
102(6)
4.3 Stinespring representation
108(5)
4.4 Kraus representation
113(4)
5 Quantum channels and operations
117(16)
5.1 Quantum operations
117(1)
5.2 Quantum channels
118(5)
5.2.1 Quantum channels in the Schrodinger picture
119(1)
5.2.2 Quantum channels in the Heisenberg picture
120(3)
5.3 Representations and dilations of channels
123(5)
5.3.1 Stinespring representation
123(1)
5.3.2 Unitary dilation
124(3)
5.3.3 Kraus representation
127(1)
5.4 Structural properties of quantum channels
128(1)
5.4.1 Convexity of channels
128(1)
5.4.2 Concatenation of channels
128(1)
5.4.3 Tensor product of channels
129(1)
5.5 Purification
129(1)
5.6 Reversible quantum channels
130(2)
5.7 Complementary channels
132(1)
6 Approximation and convergence of quantum channels
133(36)
6.1 Distinguishability of quantum states
133(12)
6.1.1 Fidelity of quantum states
133(12)
6.1.2 Bures distance
145(1)
6.2 Channel fidelity
145(4)
6.2.1 Monotonicity of channel fidelity
146(1)
6.2.2 Ensemble average and entanglement fidelities
146(3)
6.3 Norms on unconstrained channels
149(4)
6.3.1 Diamond norm
149(1)
6.3.2 Complete boundedness norm
149(2)
6.3.3 Bures distance
151(2)
6.4 Norms on constrained channels
153(6)
6.4.1 Energy-constrained operator norm
154(2)
6.4.2 Constrained diamond norms and Bures distances
156(3)
6.5 Approximations of quantum channels
159(2)
6.6 Convergences of channels
161(8)
6.6.1 Strong and uniform convergence
161(4)
6.6.2 Strong* convergence of channels
165(4)
7 Von Neumann entropy
169(34)
7.1 Von Neumann entropy on S(H)
169(2)
7.2 Properties of H(.) on S(H)
171(6)
7.3 H(.) on subsets of S(H)
177(19)
7.3.1 Closed convex subsets A c 5(H)
177(1)
7.3.2 KH(h)
178(14)
7.3.3 H(.) on an arbitrary closed subset k
192(4)
7.4 H(.) extended to L+(H)
196(7)
7.4.1 Properties of H(.) on L+(H)
197(3)
7.4.2 Discontinuity of extended quantum entropies
200(3)
8 Relative and conditional entropies
203(20)
8.1 Quantum relative entropy
203(7)
8.2 H(.||.) extended to L+(H) × (H)
210(3)
8.3 Quantum conditional entropy
213(10)
8.3.1 Definitions
213(1)
8.3.2 Properties of conditional entropy
214(9)
9 Channel output entropies
223(20)
9.1 Monotonicity of output relative entropy and Petz's theorem
223(5)
9.1.1 Monotonicity of output relative entropy
223(2)
9.1.2 Petz's theorem on output relative entropy
225(3)
9.2 Continuity of output entropies
228(11)
9.2.1 Positive linear map Φ
228(6)
9.2.2 Quantum operations
234(5)
9.3 Convex closure of output entropy
239(4)
10 Quantum entanglement
243(34)
10.1 Schmidt decomposability of states
243(7)
10.2 Separability of states
250(13)
10.2.1 Matrix of amplitudes
250(5)
10.2.2 Separability
255(8)
10.3 Measurements of entanglement
263(14)
10.3.1 Entropy of entanglement
266(3)
10.3.2 Relative entropy of entanglement
269(3)
10.3.3 Entanglement of formation
272(5)
11 Quantum mutual and coherent information
277(18)
11.1 Quantum mutual information
277(11)
11.1.1 Finite-dimensional case
284(2)
11.1.2 Infinite-dimensional case
286(2)
11.2 Coherent information
288(7)
12 Holevo X-capacity
295(44)
12.1 The x-functions
295(8)
12.1.1 Input X-function
295(1)
12.1.2 Outputs-function
296(7)
12.2 Holevo X-capacities
303(17)
12.2.1 Optimal ensembles
305(7)
12.2.2 Compact constraints
312(1)
12.2.3 Conve x constraints
313(7)
12.3 Continuity of Holevo X-capacity
320(4)
12.4 Holevo X-quantity and coherent information
324(3)
12.5 Additivity of Holevo/-capacities
327(12)
12.5.1 Hastings' counterexamples to additivity
328(1)
12.5.2 Additivity of unconstrained X-quantity
329(5)
12.5.3 Tensor product of constrained channels
334(1)
12.5.4 Additivity of constrained Holevo X-capacity
335(4)
13 Classical capacities of memoryless channels
339(44)
13.1 Transmissions of classical information
341(5)
13.1.1 Preparation of classical information
341(1)
13.1.2 Encoding and decoding of classical information
342(4)
13.2 Unconstrained classical capacity
346(9)
13.2.1 Holevo-Schumacher-Westmoreland theorem
347(1)
13.2.2 Quantum version of Feinstein's lemma
348(7)
13.3 Classical capacity of constrained channels
355(3)
13.4 Entanglement-assisted classical capacity
358(19)
13.4.1 Finite-dimensional channels
360(7)
13.4.2 Constrained infinite-dimensional channels
367(7)
13.4.3 Continuity of Cea(.): C(A, B) → (0,+ ∞)
374(3)
13.5 Comparison of classical capacities
377(6)
13.5.1 Finite-dimensional unconstrained capacities
377(2)
13.5.2 Infinite-dimensional constrained capacities
379(4)
14 Structure of quantum memory channels
383(22)
14.1 Representations of memoryless channels
384(2)
14.1.1 Kraus representation in the Schrodinger picture
384(1)
14.1.2 Kraus representation in the Heisenberg picture
385(1)
14.1.3 Unitary representation in the Schrodinger picture
385(1)
14.2 Constructive approach to memory channels
386(5)
14.2.1 Unitary representation in the Schrodinger picture
389(1)
14.2.2 Unitary representation in the Heisenberg picture
390(1)
14.2.3 Kraus representation of the memory channel
391(1)
14.3 Quasilocal algebras approach
391(6)
14.3.1 Construction of quasilocal algebras
391(3)
14.3.2 Structure of causal channels
394(3)
14.4 Forgetful channels
397(8)
14.4.1 Definition of forgetful channels
397(7)
14.4.2 Topological properties
404(1)
15 Channels with Markovian memory
405(36)
15.1 A brief review on Markov chains
405(2)
15.2 Constructions of Markov memory models
407(2)
15.3 Channels with ergodic Markovian memory
409(13)
15.3.1 Classical capacity
409(13)
15.4 Channels with general Markov memory
422(19)
15.4.1 Preamble for Markovian memory
422(7)
15.4.2 Classical capacity
429(12)
16 Channels with long-term memory
441(30)
16.1 The model
441(1)
16.2 Classical product state capacity
442(16)
16.2.1 Infinite-dimensional classical capacity
443(12)
16.2.2 Constrained classical capacity in infinite dimensions
455(3)
16.3 Entanglement-assisted classical capacity
458(13)
16.3.1 Unconstrained case
461(5)
16.3.2 Energy constrained case
466(5)
Bibliography 471(8)
Index 479
Mou-Hsiung Chang, Ph.D





PROFESSIONAL EXPERIENCE

U.S. Army Research Office (07/2002-12/2014) Basic Research Program Manager (retired 01/2015) University of Alabama in Huntsville (09/1974-07/2002) Professor Emeritus of Mathematical Sciences (09/2002-present) Chair of Mathematical Sciences Department (09/01/1993- 08/31/2001) Professor of Mathematical Sciences (09/1985 07/2002) Associate Professor of Mathematical Sciences (09/1978- 08/1985) Assistant Professor of Mathematical Sciences (09/1974 08/1978) North Carolina State University (06/2008-present) Adjunct Professor of Mathematics Massachusetts Institute of Technology (09/1984-02/1985) Visiting Scientist at MIT Laboratory for Information and Decision Systems (LIDS)