Security and privacy are often mentioned in the same breath, but they are not similar. It is a fact that both of them are important for trustworthiness of a system. However, when it comes to cloud computing, security tends to draw more attention and concern. But that does not mean that privacy can be compromised in anyway. Privacy maintenance in cloud is mainly the responsibility of service providers but consumers should also be conscious about their own privacy while drafting the service-level agreement (SLA).

Regulatory compliance is another issue that has taken a complicated shape in the context of public cloud computing facility. It often becomes difficult to fulfill all legal compliance requirements in a cloud environment where data centers of a service provider are spread across the globe and more often consumers do not know where (in which country or region) their data are being stored. Cloud consumers must be aware about their responsibilities regarding the information privacy and regulatory compliance maintenance, apart from checking service provider's reputation and approach towards maintenance of these issues.

Apart from these, this chapter discusses GRC (governance, risk and compliance) issue as another important concern of any business and how the issue becomes more prominent with adoption of cloud computing services for businesses. Regular auditing of these issues may help identify any violation. Standard audit frameworks exist, which when adopted for auditing cloud services can help build trust among the consumers.

WHAT IS PRIVACY?

Both security and privacy are interrelated but it is a misconception that privacy is a part of information security. Rather, privacy brings its own set of concerns. Privacy of personal kind of information may be very sensitive and needs special attention.

In line with the concerns about the security of a cloud system, consumers need to be careful about the privacy of their data before they use services or enter into a contract with any cloud vendor. Who owns the data? Who has access to it? How many copies are being maintained? Will the data be erased in the event the customer changes the service provider?

Computing as a utility service has been a long desired dream in the field of computing. Although the basic idea about cloud computing was introduced many years back, it could not become a reality due to several technological constraints. Later on, technologists succeeded in overcome these technical constraints one after another, and with time computing technology started advancing at a steady pace. The economical and other advantages of cloud computing were visible to everyone including business houses and once all of the required technologies were in place, the computing vendors jumped into the development of cloud services.

In last ten years, many companies have been successful in offering cloud services in different types, sizes and shapes. List of such companies include the major technology vendors like Microsoft, Amazon and Google whose cloud services have gained a major share in the market. These providers along with many other large and middle size vendors and research institutes have developed and offered a number of service plans suitable for both individual consumers and businesses.

Cloud computing is the future of computing in forthcoming years. Cloud services are rapidly gaining more and more appreciation globally and the expansion of cloud service industry is evident. It provides swift availability of enterprise-quality resource and high-performance computing services that can significantly improve business productivity. This chapter focuses on some very popular public cloud services presented by computing majors who also have contributed immensely in the development of IaaS, PaaS and SaaS.

AMAZON WEB SERVICES

Amazon.com, Inc. is an American electronic-commerce company with headquarters in Washington, United States. The company started as an online bookstore but later expanded its business in different domains. Amazon has emerged as a front-runner among the providers of public cloud services. Among the business domain of different cloud services, Amazon is considered as a market leader in Infrastructure-as-a-Service. The suite of cloud computing services offered by Amazon is known as Amazon web services (AWS).

Amazon Web Services is currently the leading IaaS offering in the market. AWS is offered through the web and has been built strictly based on SOA standards following SOAP, HTTP, REST protocols. It also uses open-source operating system and application servers.

The changing characteristics of data and need for new data processing models as well as file systems in high-performance computing environment have been discussed in previous chapters. The large data-sets produce not only structured data but un-structured data too. Storage requirement for unstructured data is entirely different from that of structured data. There is a need to maintain quicker data storage, search and retrieval as these are basic requirements in high-performance computing.

Cloud computing not only provides support for traditional DBMSs, modern data processing requirements are also catered to as well. This chapter focuses on the characteristics of this new type of databases and discusses how un-structured data are stored in those databases for efficient processing. Apart from these, the chapter also discusses about different forms of database solutions available on the high-performance cloud computing environment.

Data storage and database on the cloud is intimately tied with one another and that provides the scope for suitable solutions to optimize the database performance. This has changed the way how database is managed. Many cloud computing vendors have developed new methods of storing data objects which are different from the traditional methods of storing data.

DATABASE IN CLOUD

Consumers can avail database facility in cloud in two forms. First one is the general database solution that is implemented through installation of some database solution on IaaS (virtual machine delivered as IaaS). The other one is delivered by service providers as database-as-a-service where the vendor fully manages the backend administration jobs like installation, security management and resource assignment tasks.

In the first approach, the users can deploy database applications on cloud virtual machines like any other applications software. Apart from this, the ready-made machine images supplied by the vendors are also available with per-installed and pre-configured databases. For example, Amazon provides ready-made EC2 machine image with pre-installed Oracle Database.

In the Database-as-a-Service (DBaaS) model, the operational burden of provisioning, configuration, backup facilities are managed by the service operators.

This chapter solves the one-dimensional Schrödinger equation in a potential which (i) is constant everywhere or (ii) jumps discontinuously from one constant value to another at a finite number of points. The importance of studying such simple potentials lies in the fact that the motion of a particle in them exhibits certain exclusive quantum features, such as the possibility of finding the particle in the classically forbidden region or tunnelling through it. They also idealize several realistic potentials and provide useful insight in to the properties of the motion of a particle in realistic situations.

Constant Potential

Consider first the potential which has the same value on the entire real axis. A particle moving in such a potential would not experience any force and hence propagate freely. Without loss of generality, we take the potential to be zero. If the mass of the particle is m, then its wave function of definite energy E is the solutions of the Schroödinger equation (9.1) corresponding to U(x) = 0:

Recall from Section 8.6 that the energy of the particle cannot be less than the global minimum of the potential in which it moves. Since the potential in the present case is zero everywhere, we must have. The two linearly independent solutions of the equation above then read

This Appendix addresses the question of solving a linear ordinary second-order homogeneous differential equation

We do not go in to the conditions on the functions P(x) and Q(x) required for the equation above to admit a solution but assume that the functions possess the desired properties. The explicit solution will depend, of course, on the functional forms of P(x) and Q(x). However, before finding explicit solutions, we list below some properties of the solutions of (B.1) which are independent of the functional forms of P(x) and Q(x).

• 1. If y1(x) and y2(x) are two solutions of (B.1) then on substituting in it y(x) = ay1(x) + βy2(x), where a and b are complex numbers, it may be seen that y(x) also satisfies that equation.

• 2. Since, as shown above, any linear combination of the solutions of (B.1) is also a solution, it is sufficient to find all its linearly independent solutions. Any other solution can then be expressed as a linear combination of those linearly independent ones. To ascertain whether the solutions y1(x), y2(x) are linearly independent, assume that there exist constants A and B such that

The functions y1(x), y2(x) are linearly independent if the equation above is solved only by A = B = 0. The constants A, B are determined by forming second equation by differentiating (B.2) and solving the equation so obtained simultaneously with (B.2) by writing them as

In Chapter 15, we showed that invariance under rotation in real three-dimensional position space transforms the state of a system by a unitary transformation generated by the operator which is the sum of the orbital angular momentum operator, and the spin operator which acts on the internal state of the system. The components of obey the same commutation relations as the corresponding components of. The eigenvalue problem of the orbital angular momentum has been solved in Chapter 14 by working in the position representation. We found that the eigenvalues of are

where l = 0, 1, 2,….

However, acts on the internal state of the system and does not have position representative. Hence, for the systems having spin, we need to solve the eigenvalue problem of the angular momentum by invoking only the commutation relations between the components of, the task undertaken in this chapter. We will find that, like the orbital angular momentum, the eigenvalues of are also expressible in the form but, in addition to non-negative integral values, can be a half-odd positive integer. Thus, the spectrum of derived using the commutation relations turns out to be different from that obtained while working in position representation when permissible. This is unlike the case of harmonic oscillator for which the eigenvalues turn out to be same whether the oscillator problem is solved in the position representation (when permissible) or by using only the commutation relations between the harmonic oscillator operators.

Resource virtualization technique creates room for the adoption of dynamic approach in computing resource provisioning. The dynamic resource provisioning approach in turn creates the scope for developing scalable computing systems and applications. Scalability of systems and applications is an essential feature of cloud computing.

Computing cost depends on the total volume of resources acquired by an application. Any acquired and unutilized resource unnecessarily increases computing cost. Again, low acquisition of resource may affect application performance during higher demand. Hence, any system must run with minimum volume of required resources and should have the ability to expand itself with growing workload which is critical from business point of view. Again, a system should also have the ability to reduce itself with declining workload in terms of acquired resources. Otherwise unnecessary resource acquisition increases the cost.

This ability of expanding and shrinking of a system as per workload is known as scaling. Dynamic resource provisioning plays a key role in building of a scalable system but that alone cannot ensure the scaling. A system should also have the ability to integrate the provisioned resources effectively into itself (or release extra resources) and still run as the same system without any interruption or hitch. This ensures smooth user experience and at the same time reduces cost of computing and improves performance of applications.

WHAT IS SCALING?

Scaling is the characteristic of a system, model or function that describes its ability of growing or shrinking whenever required. In computing, scaling represents the capability of a system or application to deal with varying workload efficiently without bringing in a situation where resource shortage hampers performance or resource surplus increases the computation cost.

In simple words, scaling is defined as the ability of being enlarged (or shrunk) for accommodating growth (or fall-off) to fulfill the business needs. A system or application architecture can be termed as scalable if its performance improves on adding new resources and the improvement is proportional to the capacity added.

The emergence of cloud computing provides benefits of the utility service model to the computing users. Users of computing are now being called subscribers or consumers as they move towards cloud computing. Cloud computing is delivered to its subscribers over the internetwork as well as Internet. Subscribers can access the computing facility on subscription basis, anytime and anywhere.

The scores of benefits of cloud computing are attracting users towards it. But any new innovation comes with few challenges and cloud computing is not an exception. This chapter discusses various benefits of cloud computing and also presents the challenges before it.

The biggest challenge is related to data security and compliance issue. Most of the other critical challenges are due to the absence of open standards where vendors develop clouds using their own proprietary standard or technology. The good aspect is that, significant efforts have been undertaken to resolve all of these issues. Apart from these, this chapter briefly presents the role of web services in cloud computing development.

ORIGIN OF THE TERM ‘CLOUD COMPUTING’

The origin of the term ‘cloud computing’ dates back to the early 1990s. In those early days of network design, network engineers used to draw network diagrams representing different devices and connections among them. In such diagrams, they used to represent outer network arenas with cloud symbol since those details were not in their knowledge. This was known as ‘network cloud’ or ‘cloud’ in the networking industry during that period, but today we do not mean ‘cloud computing’ in the same sense.

With the beginning of utility computing initiatives towards the end of the last century, major software firms focussed on deliver applications over the Internet. Email services gained pace during this period as the vendors started to offer the facility to their users. And the most remarkable initiative came from Salesforce.com when they delivered business application for enterprises over the Internet in 1999. But all of these efforts were seen as part of utility computing facility development. Cloud computing did not emerge till then.

The concept of Hilbert space is at the heart of the body of quantum mechanics. In this chapter, we introduce the concept of Hilbert space and develop the algebra and calculus of operators in it. It is preceded by introduction of the notions of ‘linear vector space’ and ‘scalar product space’ on which the concept of Hilbert space is based.

Vector Space

A set V of elements {|u, |vi, |w,…g, called vectors, is said to constitute a vector space V over the field F if it is closed under the operations of addition, and multiplication by scalars in F governed by following axioms:

The symbol ji, introduced by Dirac to denote a vector, is called a ket. In the study of the representation of the vector space, we will see that a vector can be represented in different ways. A representation of interest is the one in which it is represented by a column vector. We denote column vectors by a tilde under a letter. Thus, for example,ṵ ewould represent a column vector.

Because of its properties being similar to those of the scalar zero, the null vector j0i may be denoted by the scalar 0. Whether 0 in an expression involving vectors refers to the null vector j0i or to the scalar 0 is to be inferred from the context.

The vector spaces of interest to us are:

1. If the field F in the axioms defining the vector space V is the field of real numbers, then it is called the vector space over the field of real numbers or simply a real vector space.

Cloud Computing has an alluring concept about service, and that is, it has the ability to deliver infinite resources: consumers can get any kind and any volume of resources instantly as per their demands. The somewhat incorrect idea of infinite resources in cloud computing has primarily been accomplished by creating flexible resource pools. Resource virtualization technique and auto-scaling mechanism enable an uninterrupted supply of resources during the execution of system or application.

However, if not understood properly the concept of infinite computing resources may cause serious concerns about the success of a cloud service. At the physical (data center) level, it is never possible for a cloud service provider to arrange an unlimited volume of computing resources. Service providers actually create the impression of unlimited resources before their consumers by strategic arrangement and utilization of resources. This chapter will discuss these strategies.

Earlier, the safest traditional approach in capacity planning was to buy resources for an estimated maximum capacity, which resulted in resource wastage and an unprecedented increase in budget. However with the assurance of an unlimited and dynamic supply of resources, enterprises can now plan business with minimum required resources. This reduces resource wastage as well as computing costs.

Apparently, it is the responsibility of the IaaS providers to deliver all resources as per the demand of the consumers. However without the sincere participation of the upper layer service providers (PaaS and SaaS providers) IaaS providers alone cannot make this idea successful. Even end users of cloud services (application consumers) have major roles to play. The chapter focuses on these aspects also.

WHAT IS CAPACITY PLANNING

Capacity Planning in computing is basically developing a strategy which guarantees that at any moment, the available or arranged resources will be sufficient to support the actual demand for resources and that too at the minimal possible cost. The goal of capacity planning is to identify the right amount of resource requirement to meet the service demands at present and also in the future.

Resource requirement of an application generally differs with time. A cost effective agile system can only be developed by understanding these shifting resource needs, and with proper capacity planning in place. Appropriate capacity planning made for a system offers enormous benefits.

Entanglement characterizes such correlations between the subsystems of a system which possess exclusive quantum features, in the sense to be described in this chapter. The concept of exclusive quantum features, often called quantumness, stems from the local hidden variables (LHV) theory. We describe in particular the approaches to identify the quantumness of correlations between two spin-1/2 particles. Of various such approaches, the one based on the concept of joint quasiprobability (JQP) distribution provides necessary and sufficient condition for the said identification. The quantumness of correlations between spin-1/2 particles is a resource in quantum computation and quantum information.

Entanglement

We discuss the concept of only the bipartite entanglement, i.e., entanglement between two subsystems of a system. Let the subsystems be named A and B. Let the state of the combined system A + B be described by the density operator. Let and be the operators acting only on A and only on B, respectively. If

for all and then A and B are said to be uncorrelated. The equation above will hold if

where is the density matrix of A alone and that for B alone. For a pure state of the combined system, the condition (18.2) for (18.1) to hold is equivalent with the condition