Position-momentum uncertainty relations in the presence of quantum memory
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Position-momentum uncertainty relations in the presence of quantum memory. / Furrer, Fabian ; Berta, Mario; Tomamichel, Marco; Scholz, Volkher B. ; Christandl, Matthias.
I: Journal of Mathematical Physics, Bind 55, Nr. 12, 122205, 2014.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Position-momentum uncertainty relations in the presence of quantum memory
AU - Furrer, Fabian
AU - Berta, Mario
AU - Tomamichel, Marco
AU - Scholz, Volkher B.
AU - Christandl, Matthias
PY - 2014
Y1 - 2014
N2 - A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.
AB - A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.
U2 - 10.1063/1.4903989
DO - 10.1063/1.4903989
M3 - Journal article
VL - 55
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 12
M1 - 122205
ER -
ID: 130287576