*Vlatko Vedral*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Quantum entanglement is a key resource in quantum information. Teleportation, dense coding, and many other quantum protocols rely on the existence of entanglement, and would not be possible with just ...
More

Quantum entanglement is a key resource in quantum information. Teleportation, dense coding, and many other quantum protocols rely on the existence of entanglement, and would not be possible with just classical correlations. Furthermore, using entanglement between qubits that support computation, quantum computers can solve problems faster than classical computers. Bell's inequalities can sometimes help in discriminating between entangled and separable states. However, these inequalities are not always reliable — this is true in the sense that they may fail to detect genuinely entangled states. This question is addressed in the present chapter by focusing on an entanglement witness, a Hermitian operator winch helps us to decide whether a state is entangled or not. The basic idea is that the expectation value of the witness will be different for separable and entangled states. This chapter discusses entanglement witnesses, the Jamiolkowski isomorphism, and the Peres Horodecki criterion. More examples of entanglement witnesses are given.Less

Quantum entanglement is a key resource in quantum information. Teleportation, dense coding, and many other quantum protocols rely on the existence of entanglement, and would not be possible with just classical correlations. Furthermore, using entanglement between qubits that support computation, quantum computers can solve problems faster than classical computers. Bell's inequalities can sometimes help in discriminating between entangled and separable states. However, these inequalities are not always reliable — this is true in the sense that they may fail to detect genuinely entangled states. This question is addressed in the present chapter by focusing on an entanglement witness, a Hermitian operator winch helps us to decide whether a state is entangled or not. The basic idea is that the expectation value of the witness will be different for separable and entangled states. This chapter discusses entanglement witnesses, the Jamiolkowski isomorphism, and the Peres Horodecki criterion. More examples of entanglement witnesses are given.

*Vlatko Vedral*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter explains how entanglement witnesses can be measured in practice. The main idea behind the Mach–Zehnder interferometer experiment described earlier is to test for and even measure quantum ...
More

This chapter explains how entanglement witnesses can be measured in practice. The main idea behind the Mach–Zehnder interferometer experiment described earlier is to test for and even measure quantum entanglement. The key idea is discussed along with its exact application. Partial transposition is not a physical operation because it is a positive map rather than a CP-map. Therefore, it cannot be implemented directly within the quantum formalism. However, an entanglement witness is the average of some Hermitian operator, and this average is a physically measurable quantity. Thus, it is possible to measure the effects of the partial transposition in some indirect way. This chapter discusses the implementation of the Peres Horodecki criterion using an interferometer. The important message is that a simple apparatus that measures quantum superpositions, such as a Mach–Zehnder interferometer, can also be used for much more complicated measurements.Less

This chapter explains how entanglement witnesses can be measured in practice. The main idea behind the Mach–Zehnder interferometer experiment described earlier is to test for and even measure quantum entanglement. The key idea is discussed along with its exact application. Partial transposition is not a physical operation because it is a positive map rather than a CP-map. Therefore, it cannot be implemented directly within the quantum formalism. However, an entanglement witness is the average of some Hermitian operator, and this average is a physically measurable quantity. Thus, it is possible to measure the effects of the partial transposition in some indirect way. This chapter discusses the implementation of the Peres Horodecki criterion using an interferometer. The important message is that a simple apparatus that measures quantum superpositions, such as a Mach–Zehnder interferometer, can also be used for much more complicated measurements.

*Vlatko Vedral*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the ...
More

This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.Less

This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.