Operational measures

There are [http://www.diamondlinks.net link building service] entanglement measures which are defined by certain task which should be achieved optimally by means of local operations and classical communication. They are therefore called operational measures. The most common [http://www.mycaal.com loan modification] operational measures are [[Entanglement of distillation]], [[Entanglement cost]]. [http://www.dsdmobile.com/ iphone repair] [http://www.dsdmobile.com/ iphone repair mississauga] [http://www.dsdmobile.com/ cell phone repair mississauga] [http://www.dsdmobile.com/ cell phone unlocking mississauga] Typically and operational measure involves: - input state - class of allowed operations by means of which input state should be transformed which is the class of local operations and classical communication. - output state The typical '''task''' is to obtain the greatest amount of output states given certain number of input states. Then the operational measure equals the '''optimal rate''' of number of output states that can be obtained from input states via LOCC, per number of input states (in asymptotic limit). Formally one defines operational measure as follows: Let $\backslash rho$ and $\backslash sigma$ be the input and output state. Consider a protocol i.e. sequence of LOCC operations $P\; =\; \backslash \{\; P\_n\backslash \}$ such, that $P\_n(\backslash rho^\{\backslash otimes\; n\})\; =\; \backslash tau\_n$ for each n. If $\backslash lim\_\{n\backslash rightarrow\; \backslash infty\}\; ||\backslash tau\_n\; -\; \backslash sigma^\{\backslash otimes\; m\}||=0$, we say that the protocol P achieves rate given by $R\_P(\backslash rho\; \backslash rightarrow\; \backslash sigma):=\backslash limsup\_\{n,m\; \backslash rightarrow\; \backslash infty\}\; \{m\backslash over\; n\}$. Then the operational measure $E\_\{op\}$ is defined as $E\_\{op\}(\backslash rho)=\backslash sup\_P\; R\_P(\backslash rho\backslash rightarrow\; \backslash sigma)$ In place of the input state and output state in the above definition one can consider the set of input state and the set of output states respectively. In such case the supremum in definition of $E\_\{op\}$ is taken also over input and output states. Moreover the task may by modified, so that the otput state maximises certain function (see [[Distillable key]]). [[Category: Handbook of Quantum Information]] [[Category: Entanglement]]