Quantum correlations, local interactions and error correction

Vedral, V.; Rippin, M. A.; Plenio, Martin B.

doi:10.1080/095003497152447

Cited by 7 publications

(15 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following we make special choices for D(σ||ρ). First we use an entropic measure of distance between the two density matrices, σ and ρ, also called the von Neumann relative entropy, which is defined by analogy with the classical Kullback-Leibler distance as [6,[10][11][12]:…”

Section: Local Unitary Operations Leavementioning

confidence: 99%

“…There has also been a number of papers relating the two (e.g. [5,6]). Our present work belongs to this second group.…”

mentioning

confidence: 99%

“…( 3) for pure states of the joint system ρ AB . It is known that I N cannot increase under local general measurement only [6,10], but can increase under LGM+CC showing that it cannot properly distinguish between classical and quantum mechanical correlations. The von Neumann mutual information can intuitively be understood as follows: the mutual information calculates a 'distance' between a given state ρ AB and one of its disentangled counterparts ρ A ⊗ ρ B .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Quantifying Entanglement

et al. 1997

Self Cite

View full text Add to dashboard Cite

We present conditions every measure of entanglement has to satisfy, and construct a whole class of "good" entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.[ S0031-9007(97) We have witnessed great advances in quantum information theory in recent years. There are two distinct directions in which progress is currently being made: quantum computation and error correction on the one hand (for a short survey see [1,2]), and nonlocality, Bell's inequalities, and purification, on the other hand [3,4]. There has also been a number of papers relating the two methods (e.g., [5,6]). Our present work belongs to this second group. Recently it was realized that the CHSH (ClauserHorne-Shimony-Holt) form of Bell's inequalities are not a sufficiently good measure of quantum correlations in the sense that there are states which do not violate the CHSH inequality, but, on the other hand, can be purified by local interactions and classical communications to yield a state that does violate the CHSH inequality [3]. Subsequently, it was shown that the only states of two two-level systems which cannot be purified are those that can be written as the sum over density operators which are direct product states of the two subsystems [7]. Therefore, although it is possible to say whether a quantum state is entangled or not, the amount of entanglement cannot easily be determined for general mixed states. Bennett et al. [5] have recently proposed a measure of entanglement for a general mixed state of two quantum subsystems. However, this measure has the disadvantage that it is hard to compute for a general state, even numerically. In this Letter we specify conditions which any measure of entanglement has to satisfy and construct a whole class of "good" entanglement measures. Our measures are geometrically intuitive.Unless stated otherwise, the following considerations apply to a system composed of two quantum subsystem of arbitrary dimensions. First, we define the term purification procedure more precisely. There are three distinct ingredients in any protocol that aims at increasing correlations between two quantum subsystems locally.Local general measurements (LGM).-These are performed by the two parties (A and B) separately and are described by two sets of operators satisfying the completeness relations P i A y i A i I and P j B y j B j I. The joint action of the two is described by P ij A i ≠ B j , which again describes a local general measurement.Classical communication (CC).-This means that the actions of A and B can be classically correlated. This can be described by a complete measurement on the whole space A 1 B which, as opposed to local general measurements, is not necessarily decomposable into a direct product of two operators as above, each acting on only one subsystem. If r AB is the joint state of subsyst...

show abstract

Section: Local Unitary Operations Leavementioning

confidence: 99%

“…There has also been a number of papers relating the two (e.g. [5,6]). Our present work belongs to this second group.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Quantifying Entanglement

et al. 1997

Self Cite

View full text Add to dashboard Cite

show abstract

“…Note also that the classical communication from Alice to Bob in step 2 above is crucial because otherwise the protocol would be impossible to execute (there is a deeper reason for this: if we could perform teleportation without classical communication then Alice could send messages to Bob faster than the speed of light, see e.g. [38]).…”

Section: A a Basic Description Of Teleportationmentioning

confidence: 99%

“…Although one can perform entanglement purification acting on a single pair of particles only [7,21,38], it can be shown that there are states that cannot be purified in this way [27]. Therefore we present a scheme that acts on two pairs simultaneously.…”

Section: A Entanglement Purificationmentioning

confidence: 99%

Teleportation, entanglement and thermodynamics in the quantum world

Plenio¹,

Vedral²

1998

Contemporary Physics

295

246

View full text Add to dashboard Cite

Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more particles. We will establish the basic properties of entanglement using quantum state teleportation. These principles will then allow us to formulate quantitative measures of entanglement. Finally we will show that the same general principles can also be used to prove seemingly difficult questions regarding entanglement dynamics very easily. This will be used to motivate the hope that we can construct a thermodynamics of entanglement.

show abstract

Basics of quantum computation

Vedral

Plenio

1998

Progress in Quantum Electronics

116

View full text Add to dashboard Cite

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic principles of quantum computation, including the construction of basic gates, and networks. We illustrate the power of quantum algorithms using the simple problem of Deutsch, and explain, again in very simple terms, the well known algorithm of Shor for factorisation of large numbers into primes. We then describe physical implementations of quantum computers, focusing on one in particular, the linear ion-trap realization. We explain that the main obstacle to building an actual quantum computer is the problem of decoherence, which we show may be circumvented using the methods of quantum error correction.

show abstract

Quantum correlations, local interactions and error correction

Cited by 7 publications

References 14 publications

Quantifying Entanglement

Quantifying Entanglement

Teleportation, entanglement and thermodynamics in the quantum world

Basics of quantum computation

Contact Info

Product

Resources

About