arXiv:0803.3867 · Journal of Mathematical Physics

Characterization of the sequential product on quantum effects

Stanley Gudder, Frédéric Latrémolière

Published May 1, 2008• 43 citations

Abstract

We present a characterization of the standard sequential product of quantum effects. The characterization is in terms of algebraic, continuity and duality conditions that can be physically motivated.

DOI: 10.1063/1.2904475

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arXiv:0803.3867 · Journal of Mathematical Physics

Characterization of the sequential product on quantum effects

Stanley Gudder, Frédéric Latrémolière

Published May 1, 2008• 43 citations

arXiv HTML PDF

Abstract

We present a characterization of the standard sequential product of quantum effects. The characterization is in terms of algebraic, continuity and duality conditions that can be physically motivated.

DOI: 10.1063/1.2904475

Related papers

Sequential product on standard effect algebra {\cal E} (H)

Jun Shen, Junde Wu

A quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$ , ${\cal E} (H)$ is the set of all quantum effects on $H$ . In 2001, Professor Gudder and Nagy studied the sequential product $A\circ B=A^{1/2}BA^{1/2}$ of $A, B\in {\cal E}(H)$ . In 2005, Professor Gudder asked: Is $A\circ B=A^{1/2}BA^{1/2}$ the only sequential product on ${\cal E} (H)$ ? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on ${\cal E} (H)$ ; secondly, we present a general method for constructing sequential products on ${\cal E} (H)$ ; finally, we study some properties of the sequential products constructed by the methodA quantum effect is an operator $A$ on a complex Hilbert space $H$ that satisfies $0\leq A\leq I$, ${\cal E} (H)$ is the set of all quantum effects on $H$. In 2001, Professor Gudder and Nagy studied the sequential product $A\circ B=A^{1/2}BA^{1/2}$ of $A, B\in {\cal E}(H)$. In 2005, Professor Gudder asked: Is $A\circ B=A^{1/2}BA^{1/2}$ the only sequential product on ${\cal E} (H)$? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on ${\cal E} (H)$; secondly, we present a general method for constructing sequential products on ${\cal E} (H)$; finally, we study some properties of the sequential products constructed by the method

arXiv:0905.0596Journal of Physics A Mathematical and TheoreticalAug 6, 200936 citations

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Stanley Gudder, Richard J. Greechie

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A quantum effect is an operator

A

on a complex Hilbert space

H

that satisfies

0\leq A\leq I

{\cal E} (H)

is the set of all quantum effects on

H

. In 2001, Professor Gudder and Nagy studied the sequential product

A\circ B=A^{1/2}BA^{1/2}

A, B\in {\cal E}(H)

. In 2005, Professor Gudder asked: Is

A\circ B=A^{1/2}BA^{1/2}

the only sequential product on

{\cal E} (H)

? Recently, Liu and Wu presented an example to show that the answer is negative. In this paper, firstly, we characterize some algebraic properties of the abstract sequential product on

{\cal E} (H)

; secondly, we present a general method for constructing sequential products on

{\cal E} (H)

; finally, we study some properties of the sequential products constructed by the method