Quantum dynamics of simultaneously measured non-commuting observables
Oct 5, 2016Citations per year
Abstract: (Springer)
Simultaneous measurement of two incompatible observables in a superconducting qubit placed in a cavity shows that the quantum dynamics of the system is governed by the uncertainty principle and that the wavefunction collapse is replaced by persistent diffusion. Measurements in quantum mechanics lead to collapse of the wavefunction, so measuring two incompatible variables at the same time is a much more complicated undertaking than it is in classical systems. At the same time, incompatible variables are subject to Heisenberg's uncertainty principle, so the precision with which they can be measured is fundamentally limited. These authors have developed a way of studying what happens during the simultaneous measurement of two incompatible observables in a superconducting qubit placed in a cavity. By monitoring the system continuously through non-demolition measurements, they find that the dynamics of the system is governed by the uncertainty principle and that there are distinct phases of wavefunction collapse. This finding could lead to new possibilities in quantum control, by providing different ways of steering a quantum system, and in quantum metrology, by potentially enabling simultaneous measurement of multiple incompatible properties. In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, whereas for non-commuting observables such as position and momentum Heisenberg’s uncertainty principle limits the intrinsic precision of a state. Although theoretical work1 has demonstrated that it should be possible to perform simultaneous non-commuting measurements and has revealed the limits on measurement outcomes, only recently2,3 has the dynamics of the quantum state been discussed. To realize this unexplored regime, we simultaneously apply two continuous quantum non-demolition probes of non-commuting observables to a superconducting qubit. We implement multiple readout channels by coupling the qubit to multiple modes of a cavity. To control the measurement observables, we implement a ‘single quadrature’ measurement by driving the qubit and applying cavity sidebands with a relative phase that sets the observable. Here, we use this approach to show that the uncertainty principle governs the dynamics of the wavefunction by enforcing a lower bound on the measurement-induced disturbance. Consequently, as we transition from measuring identical to measuring non-commuting observables, the dynamics make a smooth transition from standard wavefunction collapse to localized persistent diffusion and then to isotropic persistent diffusion. Although the evolution of the state differs markedly from that of a conventional measurement, information about both non-commuting observables is extracted by keeping track of the time ordering of the measurement record, enabling quantum state tomography without alternating measurements. Our work creates novel capabilities for quantum control, including rapid state purification4, adaptive measurement5,6, measurement-based state steering and continuous quantum error correction7. As physical systems often interact continuously with their environment via non-commuting degrees of freedom, our work offers a way8,9 to study how notions of contemporary quantum foundations10,11,12,13,14 arise in such settings.- Quantum mechanics
- Quantum metrology
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