Positive Operator-Valued Measures and Frames

2013 ◽  
pp. 37-60
Author(s):  
Syed Twareque Ali ◽  
Jean-Pierre Antoine ◽  
Jean-Pierre Gazeau
Keyword(s):  
Positive Operator ◽  
Positive Operator Valued Measures

Optimal quantum measurements for spin-1 and spin-3/2 particles

2001 ◽  
Vol 1 (3) ◽  
pp. 52-61
Author(s):  
P Aravind
Keyword(s):  
Positive Operator ◽  
Pure State ◽  
Quantum Measurements ◽  
Positive Operator Valued Measures ◽  
Unknown State

Positive operator valued measures (POVMs) are presented that allow an unknown pure state of a spin-1 particle to be determined with optimal fidelity when 2 to 5 copies of that state are available. Optimal POVMs are also presented for a spin-3/2 particle when 2 or 3 copies of the unknown state are available. Although these POVMs are optimal they are not always minimal, indicating that there is room for improvement.

scholarly journals Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures

2014 ◽  
Vol 90 (5) ◽  
Author(s):  
G. M. Bosyk ◽  
S. Zozor ◽  
M. Portesi ◽  
T. M. Osán ◽  
P. W. Lamberti
Keyword(s):  
Positive Operator ◽  
Geometric Approach ◽  
Uncertainty Relations ◽  
Positive Operator Valued Measures

scholarly journals Operational link between mutually unbiased bases and symmetric informationally complete positive operator-valued measures

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberto Beneduci ◽  
Thomas J. Bullock ◽  
Paul Busch ◽  
Claudio Carmeli ◽  
Teiko Heinosaari ◽  
...  
Keyword(s):  
Positive Operator ◽  
Mutually Unbiased Bases ◽  
Positive Operator Valued Measures

scholarly journals Probing qubit by qubit: Properties of the POVM and the information/disturbance tradeoff

2014 ◽  
Vol 12 (02) ◽  
pp. 1461012 ◽  
Author(s):  
Carlo Sparaciari ◽  
Matteo G. A. Paris
Keyword(s):  
Positive Operator ◽  
Projective Measurement ◽  
Matrix Elements ◽  
Positive Operator Valued Measures ◽  
Unitary Coupling ◽  
Probe System ◽  
Initial Preparation ◽  
Free Parameters

We address the class of positive operator-valued measures (POVMs) for qubit systems that are obtained by coupling the signal qubit with a probe qubit and then performing a projective measurement on the sole probe system. These POVMs, which represent the simplest class of qubit POVMs, depends on 3 + 3 + 2 = 8 free parameters describing the initial preparation of the probe qubit, the Cartan representative of the unitary coupling, and the projective measurement at the output, respectively. We analyze in some detail the properties of the POVM matrix elements, and investigate their values for given ranges of the free parameters. We also analyze in detail the tradeoff between information and disturbance for different ranges of the free parameters, showing, among other things, that (i) typical values of the tradeoff are close to optimality and (ii) even using a maximally mixed probe one may achieve optimal tradeoff.

scholarly journals Natural Quantum Operational Semantics with Predicates

2008 ◽  
Vol 18 (3) ◽  
pp. 341-359 ◽  
Author(s):  
Marek Sawerwain ◽  
Roman Gielerak
Keyword(s):  
Positive Operator ◽  
Operational Semantics ◽  
General Definition ◽  
Completely Positive Maps ◽  
Transition Systems ◽  
Positive Operator Valued Measures ◽  
Labelled Transition Systems ◽  
Positive Maps ◽  
Definition Of ◽  
Positive Operator Valued Measure

Natural Quantum Operational Semantics with PredicatesA general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.

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