Negative Quantum Channels: An Introduction to Quantum Maps by James M. McCracken

By James M. McCracken

This ebook is a short advent to destructive quantum channels, i.e., linear, trace-preserving (and constant) quantum maps that aren't thoroughly confident. The flat and sharp operators are brought and defined. entire positivity is gifted as a mathematical estate, however it is argued that entire positivity isn't really a actual requirement of all quantum operations. Negativity, a degree of the inability of whole positivity, is proposed as a device for empirically checking out whole positivity assumptions.

Show description

Read Online or Download Negative Quantum Channels: An Introduction to Quantum Maps that are Not Completely Positive PDF

Best quantum physics books

Quantum finance: path integrals and Hamiltonians for options

Monetary arithmetic is at present virtually thoroughly ruled by means of stochastic calculus. offering a totally self sufficient procedure, this publication applies the mathematical and conceptual formalism of quantum mechanics and quantum box idea (with specific emphasis at the direction fundamental) to the idea of techniques and to the modeling of rates of interest.

Quantum theory of optical coherence

A precis of the pioneering paintings of Glauber within the box of optical coherence phenomena and photon statistics, this e-book describes the basic rules of recent quantum optics and photonics in an academic type. it really is therefore not just meant as a reference for researchers within the box, but additionally to provide graduate scholars an perception into the elemental theories of the sector.

Quantum Chemistry: The Development of Ab Initio Methods in Molecular Electronic Structure Theory

For every of one hundred fifty landmark papers in ab initio molecular digital constitution equipment, the writer presents a lucid remark. the first concentration is technique, instead of specific chemical difficulties. the chosen papers current very important tools and illustrate their effectiveness in predicting various chemical phenomena.

Extra resources for Negative Quantum Channels: An Introduction to Quantum Maps that are Not Completely Positive

Sample text

Specifically, we will use constructors to take vectors of states to superoperators or specific kinds of matrices. 13 For example, a superoperator S constructed using the tomography vector E would be written using some superoperator constructor S as S DSˇE : e columns of S will be defined by “columnized”¹¹ versions of linear combinations of the members of E . e superoperator S is a matrix of complex values constructed from rearranged elements ¹¹e concept of columnizing matrices will be discussed in depth in the next section.

4j j D 1 ˙ c0 C c1 C c2 2c0 c3 C c3 0 : 2 2 e main idea of tomography is to find a complete description of the qubit channel using only valid states that can be created in the lab. Consider the following example. 6 e experimentalist might be looking for the state  à a b D c d 32 2. TOMOGRAPHY that can be written down as  à  à  à  à 1 0 0 1 0 0 0 0 Da Cb Cc Cd : 0 0 0 0 1 0 0 1 e matrices associated with the coefficients a and d are valid density matrices ( 0 and 1 , respectively) and can, therefore, be created in the lab.

ED. ˝ 1; ˝ 2; ˝ 3; ˝ 4/ and E˝ D. x1 ˙ y1 ; x2 ˙ y2 ; x3 ˙ y3 ; x4 ˙ y4 / : e dot product of a vector of states with a vector of complex numbers is defined in analogy to the normal dot product between vectors as cE E D 4 X i ci i D c1 1 C c2 2 C c3 3 C c4 4 ; where E is a qubit vector of states and cE is a vector of complex numbers. A superoperator is a linear operator that takes an operator to another operator. , to take density operators to other density operators). 12 It will be shown in the next section that a superoperator representing a quantum channel can be completely characterized in the lab using the states in a tomography vector.

Download PDF sample

Rated 4.16 of 5 – based on 4 votes