Mixed-State Entanglement and Quantum Communication

Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard

doi:10.1007/3-540-44678-8_5

Cited by 100 publications

(113 citation statements)

References 107 publications

Supporting

Mentioning

109

Contrasting

Order By: Relevance

“…As can be verified using the Positive Partial Transposition (PPT) criterion [55,56], this state is entangled if and only if p > p Ent ≡ 1/(d + 1). Using the procedures outlined in Sec.…”

Section: A Bell-chsh Violation For Two-qudit Statesmentioning

confidence: 99%

Bounds on quantum correlations in Bell-inequality experiments

Liang

Doherty

2007

Phys. Rev. A

View full text Add to dashboard Cite

Bell-inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state and Bell inequality, both a lower bound and an upper bound on the maximal violation of the inequality. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.

show abstract

“…As can be verified using the Positive Partial Transposition (PPT) criterion [55,56], this state is entangled if and only if p > p Ent ≡ 1/(d + 1). Using the procedures outlined in Sec.…”

Section: A Bell-chsh Violation For Two-qudit Statesmentioning

confidence: 99%

Bounds on quantum correlations in Bell-inequality experiments

Liang

Doherty

2007

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Therefore it is important to get a more accurate description of entanglement, especially for higher dimensional systems, which includes detecting and measuring entanglement (for an overview see, e.g., Refs. [5,6]). For pure states such a description is rather simple whereas for mixed states it is is more complicated.…”

Section: Introductionmentioning

confidence: 99%

Optimal entanglement witnesses for qubits and qutrits

et al. 2005

View full text Add to dashboard Cite

We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular 2-qubit and 2-qutrit states -and their generalizations to arbitrary dimensions -where we calculate the optimal entanglement witnesses explicitly.

show abstract

“…Much effort has been made in studying the mathematical structure of entanglement, especially the quantification of entanglement (see, for instance, Refs. [12,13]). There exist different kinds of measures of entanglement indicating somehow the difference between entangled and separable states, which is usually related to the entropy of the states (see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Geometric picture of entanglement and Bell inequalities

2002

View full text Add to dashboard Cite

We work in the real Hilbert space H s of hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S ⊂ H s of separable states. This violation equals the euclidean distance in H s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

show abstract

Mixed-State Entanglement and Quantum Communication

Cited by 100 publications

References 107 publications

Bounds on quantum correlations in Bell-inequality experiments

Bounds on quantum correlations in Bell-inequality experiments

Optimal entanglement witnesses for qubits and qutrits

Geometric picture of entanglement and Bell inequalities

Contact Info

Product

Resources

About