A famous result by Alan Turing dating back to 1936 is that a general algorithm solving the halting problem on a Turing machine for all possible inputs and programs cannot exist - the halting problem is undecidable. Formally, an undecidable problem is a decision problem for which one cannot construct a single algorithm that will always provide a correct answer in finite time. In this work, we show that surprisingly, very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable.
Nature Communications, 2, 231 (2011)
Microscale and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example, in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavours. Their performance is in many cases limited by the deleterious effects of mechanical damping. In this study, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators.
Optical interferometry is amongst the most sensitive techniques for precision measurement. By increasing the light intensity a more precise measurement can usually be made. However, in some applications the sample is light sensitive. By using entangled states of light the same precision can be achieved with less exposure of the sample. This concept has been demonstrated in measurements of fixed, known optical components.
The detection of a nuclear spin in an individual molecule represents a key challenge in physics and biology whose solution has been pursued for many years. The small magnetic moment of a single nucleus and the unavoidable environmental noise present the key obstacles for its realization.
Phys. Rev. Lett. 108, 120503 (2012)
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard), both for classical and quantum mechanical systems.
Nature, 478, 89–92 (2011)
The simple mechanical oscillator, canonically consisting of a coupled massspring system, is used in a wide variety of sensitive measurements, including the detection of weak forces1 and small masses2. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion.
The experimental violation of Bell inequalities using spacelike separated measurements precludes the explanation of quantum correlations through causal influences propagating at subluminal speed. Yet, it is always possible, in principle, to explain such experimental violations through models based on hidden influences propagating at a finite speed v>c, provided v is large enough. Here, we show that for any finite speed v>c, such models predict correlations that can be exploited for faster-than-light communication.
We argue that thermal machines can be understood from the perspective of `virtual qubits' at `virtual temperatures': The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines.
J. Phys. A: Math. Theor. 44, 492001 (2011)
Phys. Rev. Lett. 107, 207209 (2011)
We exploit the geometry of a zig-zag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics.