TY - JOUR

T1 - Minimum-cost quantum measurements for quantum information

AU - Wallden, Petros

AU - Dunjko, Vedran

AU - Andersson, Erika

PY - 2014/3/28

Y1 - 2014/3/28

N2 - Knowing about optimal quantum measurements is important for many applications in quantum information and quantum communication. However, deriving optimal quantum measurements is often difficult. We present a collection of results for minimum-cost quantum measurements, and give examples of how they can be used. Among other results, we show that a minimum-cost measurement for a set of given pure states is formally equivalent to a minimum-error measurement for certain mixed states of those same pure states. For pure symmetric states it turns out that for a certain class of cost matrices, the minimum-cost measurement is the square-root measurement. That is, the optimal minimum-cost measurement is in this case the same as the minimum-error measurement. These results are in agreement with Nakahira and Usuda (2012 Phys. Rev. A 86 062305). Finally, we consider sequences of individual uncorrelated systems, and examine when the global minimum-cost measurement is a sequence of optimal local measurements. We consider an example where the global minimum-cost measurement is, perhaps counter-intuitively, not a sequence of local measurements, and discuss how this is related to the Pusey–Barrett–Rudolph argument for the nature of the wave function.

AB - Knowing about optimal quantum measurements is important for many applications in quantum information and quantum communication. However, deriving optimal quantum measurements is often difficult. We present a collection of results for minimum-cost quantum measurements, and give examples of how they can be used. Among other results, we show that a minimum-cost measurement for a set of given pure states is formally equivalent to a minimum-error measurement for certain mixed states of those same pure states. For pure symmetric states it turns out that for a certain class of cost matrices, the minimum-cost measurement is the square-root measurement. That is, the optimal minimum-cost measurement is in this case the same as the minimum-error measurement. These results are in agreement with Nakahira and Usuda (2012 Phys. Rev. A 86 062305). Finally, we consider sequences of individual uncorrelated systems, and examine when the global minimum-cost measurement is a sequence of optimal local measurements. We consider an example where the global minimum-cost measurement is, perhaps counter-intuitively, not a sequence of local measurements, and discuss how this is related to the Pusey–Barrett–Rudolph argument for the nature of the wave function.

U2 - 10.1088/1751-8113/47/12/125303

DO - 10.1088/1751-8113/47/12/125303

M3 - Article

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 12

ER -