Continuous decomposition of quantum measurements via Hamiltonian feedback

Florjanczyk, Jan; Brun, Todd A.

doi:10.1103/physreva.92.062113

Cited by 3 publications

(4 citation statements)

References 14 publications

(14 reference statements)

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“…Ahn et al [12] investigated using continuous-time quantum measurements for this purpose, thus pioneering a fruitful line of research [13][14][15][16][17][18][19][20][21]. Feedback control additionally allows one to view weak measurements as building blocks for constructing other generalized measurements, as explored by Brun and collaborators [22][23][24][25]. Continuous weak measurements have also been pressed into service for parameter and state estimation [26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

Gross

Caves

Milburn

et al. 2018

Quantum Sci. Technol.

117

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In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.

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Section: Introductionmentioning

confidence: 99%

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

Gross

Caves

Milburn

et al. 2018

Quantum Sci. Technol.

117

View full text Add to dashboard Cite

show abstract

“…A feature worth pointing out in continuous measurements is the use of an adaptive procedure that updates the current status for the next step of measurement. This feedback technique has both experimental advantage for practical designs [14][15][16][17][18] and theoretical importance for the ability to realize more general classes of quantum measurements [19][20][21][22]. In quantum optics, for example, the phase measurement of a single mode can be improved by feedback loops during the measurement process [14,15], and it was also used in the preparation and stabilization of photon number states [16].…”

Section: Introductionmentioning

confidence: 99%

“…It is also well-known that any generalized measurement for a system is equivalent to letting the system interact with an ancilla followed by a projective measurement on the ancilla. In [21,22], it is shown that what classes of generalized measurements can be achieved by tuning the probe state or the interaction Hamiltonian during the continuous measurement process.…”

Section: Introductionmentioning

confidence: 99%

Qubit positive-operator-valued measurements by destructive weak measurements

Chen

Brun

2019

Phys. Rev. A

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Many quantum measurements, such as photodetection, can be destructive. In photodetection, when the detector "clicks" a photon has been absorbed and destroyed. Yet the lack of a click also gives information about the presence or absence of a photon. In monitoring the emission of photons from a source, one decomposes the strong measurement into a series of weak measurements, which describe the evolution of the state during the measurement process. Motivated by this example of destructive photon detection, a simple model of destructive weak measurements using qubits was studied in earlier work by the authors. It has shown that the model can achieve any positive-operator-valued measurement (POVM) with commuting POVM elements including projective measurements. In this paper, we use a different approach for decomposing any POVM into a series of weak measurements. The process involves three steps: randomly choose, with certain probabilities, a set of linearly independent POVM elements; perform that POVM by a series of destructive weak measurements; output the result of the series of weak measurements with certain probabilities. The probabilities of the outcomes from this process agree with those from the original POVM, and hence this model of destructive weak measurements can perform any qubit POVM. arXiv:1812.00425v2 [quant-ph]

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“…A more powerful model [8] again characterizes the set of generalized measurements that can be decomposed into a sequence of weak measurements based on interactions between a stream of qubit probes and the system, but now the interaction Hamiltonian between them can itself be varied based on the feedback. The work in [8] assumes that the interaction Hamiltonian is a linear combination of some fixed set of Hamiltonian terms. The achievable measurements in this model have measurement operators from a finite dimensional Jordan algebra within the span of the Hamiltonian terms.…”

Section: Introductionmentioning

confidence: 99%

Decomposing qubit positive-operator-valued measurements into continuous destructive weak measurements

Chen

Brun

2018

Phys. Rev. A

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It has been shown that any generalized measurement can be decomposed into a sequence of weak measurements corresponding to a stochastic process. However, the weak measurements may require almost arbitrary unitaries, which are unlikely to be realized by any real measurement device. Furthermore, many measurement processes are destructive, like photon counting procedures that terminate once all photons are consumed. One cannot expect to have full control of the evolution of a state under such destructive measurements, and the possible unitaries allow only a limited set of weak measurements. In this paper, we consider a qubit model of destructive weak measurements, which is a toy version of an optical cavity, in which the state of an electromagnetic field mode inside the cavity leaks out and is measured destructively while the vacuum state |0 leaks in to the cavity. At long times, the state of the qubit inevitably evolves to be |0 , and the only available control is the choice of measurement on the external ancilla system. Surprisingly, this very limited model can still perform an arbitrary projective measurement on the qubit in any basis, where the probability of getting an outcome satisfies the usual Born rule. Combining this method with probabilistic post processing, the result can be extended to any generalized measurement with commuting POVM elements. This implies, among other results, that any two-outcome POVM on a qubit can be decomposed into a sequence of destructive weak measurements by this restricted measurement device.

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Continuous decomposition of quantum measurements via Hamiltonian feedback

Cited by 3 publications

References 14 publications

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

Qubit models of weak continuous measurements: markovian conditional and open-system dynamics

Qubit positive-operator-valued measurements by destructive weak measurements

Decomposing qubit positive-operator-valued measurements into continuous destructive weak measurements

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