Entanglement cost of generalised measurements

Details Entanglement cost of generalised measurements Entanglement cost of generalised measurements

2003-03-27

arxiv.org/abs/quant-ph/0303167v1

Physics

Quantum Physics

20 pages, plain latex

Scientific paper

Bipartite entanglement is one of the fundamental quantifiable resources of quantum information theory. We propose a new application of this resource to the theory of quantum measurements. According to Naimark's theorem any rank 1 generalised measurement (POVM) M may be represented as a von Neumann measurement in an extended (tensor product) space of the system plus ancilla. By considering a suitable average of the entanglements of these measurement directions and minimising over all Naimark extensions, we define a notion of entanglement cost E_min(M) of M. We give a constructive means of characterising all Naimark extensions of a given POVM. We identify various classes of POVMs with zero and non-zero cost and explicitly characterise all POVMs in 2 dimensions having zero cost. We prove a constant upper bound on the entanglement cost of any POVM in any dimension. Hence the asymptotic entanglement cost (i.e. the large n limit of the cost of n applications of M, divided by n) is zero for all POVMs. The trine measurement is defined by three rank 1 elements, with directions symmetrically placed around a great circle on the Bloch sphere. We give an analytic expression for its entanglement cost. Defining a normalised cost of any d-dimensional POVM by E_min(M)/log(d), we show (using a combination of analytic and numerical techniques) that the trine measurement is more costly than any other POVM with d>2, or with d=2 and ancilla dimension 2. This strongly suggests that the trine measurement is the most costly of all POVMs.

Affiliated with

Also associated with

No associations

Rating

Entanglement cost of generalised measurements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entanglement cost of generalised measurements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entanglement cost of generalised measurements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-133208