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arXiv:1112.0276 · Physical Review A

Extraction of information from a single quantum

Gheorghe Sorin Paraoanu

Published Apr 18, 2011• 17 citations
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Abstract

We investigate the possibility of performing quantum tomography on a single qubit with generalized partial measurements and the technique of measurement reversal. Using concepts from statistical decision theory, we prove that, somewhat surprisingly, no information can be obtained using this scheme. It is shown that, irrespective of the measurement technique used, extraction of information from single quanta is at odds with other general principles of quantum physics.

DOI
10.1103/physreva.83.044101

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We investigate the possibility of performing quantum tomography on a single qubit with generalized partial measurements and the technique of measurement reversal. Using concepts from statistical decision theory, we prove that, somewhat surprisingly, no information can be obtained using this scheme. It is shown that, irrespective of the measurement technique used, extraction of information from single quanta is at odds with other general principles of quantum physics.
We introduce a type of measurements which generalize the so-called "partial measurements" performed in recent years with phase qubits. While in the case of partial measurements it has been demonstrated that one could undo the effect of the measurement only for non-switching events, we show here that generalized partial measurements can be reversed probabilistically for both switching and non-switching events. We calculate the associated Fisher information and discuss the estimation sensitivity for quantum tomography. Two ways of implementing this type of measurements with superconducting qubits are proposed.
We explore the possibility of using ``weak'' measurements to carry out quantum state tomography via numerical simulations. Given a fixed number of copies of identically prepared states of a qubit, we perform state tomography using weak as well as projective measurements. Due to the collapse of the state after measurement, we cannot reuse the state after a projective measurement. If the coupling strength between the quantum system and the measurement device is made weaker, the disturbance caused to the state can be lowered. This then allows us to reuse the same member of the ensemble for further measurements and thus extract more information from the system. However, this happens at the cost of getting imprecise information from the first measurement. We implement this scheme for a single qubit and show that under certain circumstances, it can outperform the projective measurement-based tomography scheme. This opens up the possibility of new ways of extracting information from quantum ensembles. We study the efficacy of this scheme for different coupling strengths and different ensemble sizes.
We explore the use of weak quantum measurements for single-qubit quantum state tomography processes. Weak measurements are those where the coupling between the qubit and the measurement apparatus is weak; this results in the quantum state being disturbed less than in the case of a projective measurement. We employ a weak measurement tomography protocol developed by Das and Arvind, which they claim offers a new method of extracting information from quantum systems. We test the Das-Arvind scheme for various measurement strengths, and ensemble sizes, and reproduce their results using a sequential stochastic simulation. Lastly, we place these results in the context of current understanding of weak and projective measurements.
Observational entropy is interpreted as the uncertainty an observer making measurements associates with a system. So far, however, properties that make such an interpretation possible relied on the assumption of projective measurements. Here we show that the same properties hold even when considering general measurements (POVMs), and therefore such an interpretation stands completely generally. This means that this quantity serves as a test of how powerful a given series of measurements is in information extraction. We make use of this interpretation and by calculating observational entropy we demonstrate how different indirect measurement schemes, which are those using a probe, compare with a direct measurement. In particular, we find that any pure state can be perfectly determined using a two-dimensional probe. We also compare different von Neumann measurement schemes, in which the probe is a heavy particle, and demonstrate which scheme performs the best under which circumstances. Finally, we connect observational entropy with quantum tomography, and give it its operational meaning. Further developed, this quantity could find wide applications in quantum information processing, and help with determining the best read out procedures for quantum memories and computation outputs of quantum computers.