In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to account for the effects of the measurement back action. To this end, we derive a quantum analog of the Euler relation, which is governed by the information retrieved by local quantum measurements. The validity of the relation is demonstrated for the collective dissipation model, where we find that thermodynamic behavior is exhibited in the weak-coupling regime.

arXiv:2106.04459EntropyJul 13, 20212 citations

Hierarchical incompatibility measures in multi-parameter quantum estimation

Hongzhen Chen, Yu Chen, Haidong Yuan

When collective measurements on an infinite number of copies of identical quantum states can be performed, the precision limit of multi-parameter quantum estimation is quantified by the Holevo bound. In practice, however, the collective measurements are always restricted to a finite number of quantum states, under which the precision limit is still poorly understood. Here we provide an approach to study the multi-parameter quantum estimation with general $p$ -local measurement where the collective measurements are restricted to at most $p$ copies of quantum states. We demonstrate the power of the approach by providing a hierarchy of nontrivial tradeoff relations for multi-parameter quantum estimation which quantify the incompatibilities of general $p$ -local measurement. These tradeoff relations also provide a necessary condition for the saturation of the quantum Cramer-Rao bound under $p$ -local measurement, which is shown reducing to the weak commutative condition when $p\rightarrow \infty$ . To further demonstrate the versatility of the approach, we also derive another set of tradeoff relations in terms of the right logarithmic operators(RLD).When collective measurements on an infinite number of copies of identical quantum states can be performed, the precision limit of multi-parameter quantum estimation is quantified by the Holevo bound. In practice, however, the collective measurements are always restricted to a finite number of quantum states, under which the precision limit is still poorly understood. Here we provide an approach to study the multi-parameter quantum estimation with general $p$-local measurement where the collective measurements are restricted to at most $p$ copies of quantum states. We demonstrate the power of the approach by providing a hierarchy of nontrivial tradeoff relations for multi-parameter quantum estimation which quantify the incompatibilities of general $p$-local measurement. These tradeoff relations also provide a necessary condition for the saturation of the quantum Cramer-Rao bound under $p$-local measurement, which is shown reducing to the weak commutative condition when $p\rightarrow \infty$. To further demonstrate the versatility of the approach, we also derive another set of tradeoff relations in terms of the right logarithmic operators(RLD).

Sep 13, 20213 citations

Local relativistic quantum physics

Rudolf Haag

Physica A Statistical Mechanics and its ApplicationsMar 1, 198425 citations

Symmetry constraints on temporal order in measurement-based quantum computation

R. Raussendorf, P. Sarvepalli, T.-C. Wei +1 more

We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid. Conversely, we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant.We discuss the interdependence of resource state, measurement setting and temporal order in measurement-based quantum computation. The possible temporal orders of measurement events are constrained by the principle that the randomness inherent in quantum measurement should not affect the outcome of the computation. We provide a classification for all temporal relations among measurement events compatible with a given initial stabilizer state and measurement setting, in terms of a matroid. Conversely, we show that classical processing relations necessary for turning the local measurement outcomes into computational output determine the resource state and measurement setting up to local equivalence. Further, we find a symmetry transformation related to local complementation that leaves the temporal relations invariant.

arXiv:1210.0620Electronic Proceedings in Theoretical Computer ScienceOct 1, 20125 citations

p

-local measurement where the collective measurements are restricted to at most

p

copies of quantum states. We demonstrate the power of the approach by providing a hierarchy of nontrivial tradeoff relations for multi-parameter quantum estimation which quantify the incompatibilities of general

p

-local measurement. These tradeoff relations also provide a necessary condition for the saturation of the quantum Cramer-Rao bound under

p

-local measurement, which is shown reducing to the weak commutative condition when

p\rightarrow \infty

. To further demonstrate the versatility of the approach, we also derive another set of tradeoff relations in terms of the right logarithmic operators(RLD).