Macroscopic superpositions require tremendous measurement devices

We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such as generated in previous experiments this is not a stringent restriction, for macroscopic superpositions of the size of a cat the required effort quickly becomes intractable, requiring measurement devices of the size of the Earth. We illustrate our results using macroscopic superposition states of photons, spins, and position. Finally, we also show how this limitation can be circumvented by dealing with superpositions in relative degrees of freedom.Comment: 20 pages (including appendices), 1 Figur

Adaptive quantum metrology under general Markovian noise

We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as $1/T$, where $T$ is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most $1/\sqrt{T}$ scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the $1/T$ precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.Comment: 13 pages, see also arXiv:1706.0244

Towards loophole-free Bell inequality test with preselected unsymmetrical singlet states of light

Can a Bell test with no detection loophole be demonstrated for multi-photon entangled states of light within the current technology? We examine the possibility of a postselection-free CHSH-Bell inequality test wih an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed to be not useful for this purpose.Comment: 12 pages, 8 figures, accepted to Phys. Rev.

Noisy distributed sensing in the Bayesian regime

We consider non-local sensing of scalar signals with specific spatial dependence in the Bayesian regime. We design schemes that allow one to achieve optimal scaling and are immune to noise sources with a different spatial dependence than the signal. This is achieved by using a sensor array of spatially separated sensors and constructing a multi-dimensional decoherence free subspace. While in the Fisher regime with sharp prior and multiple measurements only the spectral range $\Delta$ is important, in single-shot sensing with broad prior the number of available energy levels $L$ is crucial. We study the influence of $L$ and $\Delta$ also in intermediate scenarios, and show that these quantities can be optimized separately in our setting. This provides us with a flexible scheme that can be adapted to different situations, and is by construction insensitive to given noise sources.Comment: 9 pages, 1 figur

Proposal for witnessing non-classical light with the human eye

We give a complete proposal showing how to detect the non-classical nature of photonic states with naked eyes as detectors. The enabling technology is a sub-Poissonian photonic state that is obtained from single photons, displacement operations in phase space and basic non-photon-number-resolving detectors. We present a detailed statistical analysis of our proposal including imperfect photon creation and detection and a realistic model of the human eye. We conclude that a few tens of hours are sufficient to certify non-classical light with the human eye with a p-value of 10%.Comment: 9 pages, 5 figures, accepted versio

Noisy pre-processing facilitating a photonic realisation of device-independent quantum key distribution

Device-independent quantum key distribution provides security even when the equipment used to communicate over the quantum channel is largely uncharacterized. An experimental demonstration of device-independent quantum key distribution is however challenging. A central obstacle in photonic implementations is that the global detection efficiency, i.e., the probability that the signals sent over the quantum channel are successfully received, must be above a certain threshold. We here propose a method to significantly relax this threshold, while maintaining provable device-independent security. This is achieved with a protocol that adds artificial noise, which cannot be known or controlled by an adversary, to the initial measurement data (the raw key). Focusing on a realistic photonic setup using a source based on spontaneous parametric down conversion, we give explicit bounds on the minimal required global detection efficiency.Comment: 5+16 pages, 4 figure