Author(s): Mikko Tukiainen

The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables.…

[Phys. Rev. A 95, 012127] Published Fri Jan 20, 2017

# Noncommutative geometrical origin of the energy-momentum dispersion relation. (arXiv:1611.05810v2 [math-ph] UPDATED)

## hep-th updates on arXiv.org

Authors: Apimook Watcharangkool, Mairi Sakellariadou

We investigate a link between the energy-momentum dispersion relation and the spectral distance in the context of a Lorentzian almost-commutative spectral geometry, defined by the product of Minkowski spacetime and an internal discrete noncommutative space. Using the causal structure, the almost-commutative manifold can be identified with a pair of four-dimensional Minkowski spacetimes embedded in a five-dimensional Minkowski geometry. Considering fermions travelling within the light cone of the ambient five-dimensional spacetime, we then derive the energy-momentum dispersion relation.

# Operator of Time and Generalized Schroedinger Equation. (arXiv:1701.05244v1 [quant-ph])

## gr-qc updates on arXiv.org

Authors: Slobodan Prvanovic

Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator of the change of energy while the operator of energy, that is conjugate to the operator of time, generates time evolution in this proposal. Two examples, one with discrete time and the other with continuous one, are given and the generalization of Schroedinger equation is proposed.

# Is there a quantum limit on speed of computation?. (arXiv:1701.05550v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: N. A. Sinitsyn

I argue that access to quantum memory allows information processing with arbitrarily weak control signals. So, there is a class of computational problems that can be solved without speed limit at finite energy input.

# Quantum mechanics for non-inertial observers. (arXiv:1701.04298v1 [quant-ph])

## gr-qc updates on arXiv.org

Authors: Marko Toroš, André Großardt, Angelo Bassi

A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass motion of a quantum system subject to gravity can be derived more rigorously, addressing the ambiguous definition of relativistic center-of-mass coordinates. We further demonstrate that, contrary to the prediction by Pikovski et al., external forces play a crucial role in the relativistic coupling of internal and external degrees of freedom, resulting in a complete cancellation of the alleged coupling in Earth-bound laboratories for systems supported against gravity by an external force. We conclude that the proposed decoherence effect is an effect of relative acceleration between quantum system and measurement device, rather than a universal effect in gravitational fields.

# Measuring complementary observables on quantum clones. (arXiv:1701.04095v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: G. S. Thekkadath, R. Y. Saaltink, L. Giner, J. S. Lundeen

Determining an unknown quantum state requires measurements that cannot be performed precisely at the same time, i.e. jointly, since they disturb one another. As a result, it is not possible to determine the state with only a single copy of the system. A simplistic strategy to sidestep the disturbance is to make copies of the state and instead perform each measurement on a separate copy. However, it is fundamentally impossible to make an exact copy of an unknown quantum state. In fact, the security of promising quantum technologies such as quantum cryptography are built upon this very principle. It is interesting to ask what can be learned from a joint measurement of incompatible observables on the best copies allowed by quantum mechanics (“clones”). Here, we show that by measuring complementary observables (e.g. position and momentum) on the output of an optimal cloner, we can determine the quantum state of the system. In particular, we produce two clones of a polarized photon and jointly measure two complementary polarization observables, one on each clone. This work demonstrates the intimate and fundamental connections between determining quantum states, joint measurements, and cloning in quantum mechanics. The method can be implemented with a single quantum logic gate and requires measuring only two observables, thus providing a practical tool for determining high-dimensional quantum states.

# Revealing photons’ past via quantum twisted double-slit experiment. (arXiv:1701.04081v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: Zhi-Yuan Zhou, Zhi-Han Zhu, Shi-Long Liu, Yin-Hai Li, Shuai Shi, Dong-Sheng Ding, Li-Xiang Chen, Wei Gao, Guang-Can Guo, Bao-Sen Shi

Are quantum states real? How to think about this the most important, most fundamental and most profound question in quantum mechanics still has not been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayed-choice experiments. The heart of the matter comes down to what can describe physical reality if wavefunctions cannot. Here, to address this long-standing issue, we present a quantum twisted double-slit experiment, in which orbital angular momentum degree-of-freedom is employed to ‘mark’ the double slits (mimicked by spatial light modulators). Besides providing a which-slit observation interface, by exploiting the variable arrival time ascribed to the subluminal feature of twisted photons, the behavior of a photon during its time in flight is revealed for the first time. We found that the arrival time of photons does not accord with the states obtained in measurements, but agree well with the theoretical predictions calculated from their wavefunctions during the propagation. Our results demonstrate that wavefunctions describes a realistic manner of quantum entities’ existence and evolution rather than only a mathematical abstraction for only providing a probability list of measurement outcomes. This finding makes an important update in understanding the role of wavefunctions in the evolution of quantum entities, inspires a new insight on nonlocality and wave-particle duality, and reminds us there is a neglected powerful resource for quantum science needing revisit.

Authors: Gabriel Cozzella, Andre G. S. Landulfo, George E. A. Matsas, Daniel A. T. Vanzella

The Unruh effect — according to which linearly accelerated observers with proper acceleration a= constant in the (no-particle) vacuum state of inertial observers experience a thermal bath of particles with temperature $T_U = a \hbar / (2 \pi k_B c)$ — has just completed its 40$^{th}$ anniversary. A ‘direct’ experimental confirmation of the Unruh effect has been seen with concern because the linear acceleration needed to reach a temperature $1 K$ is of order $10^{20} m/s^2$. Although the Unruh effect can be rigorously considered as well tested as free quantum field theory itself, it would be satisfying to observe some lab phenomenon which could evidence its existence. Here, we propose a simple experiment reachable under present technology whose result may be directly interpreted in terms of the Unruh thermal bath. Then, instead of waiting for experimentalists to perform the experiment, we use standard classical electrodynamics to anticipate its output and show that it reveals the presence of a thermal bath with temperature $T_U$ in the accelerated frame. Unless one is willing to question the validity of classical electrodynamics, this must be seen as a virtual observation of the Unruh effect.

# Guaranteed recovery of quantum processes from few measurements. (arXiv:1701.03135v1 [quant-ph])

## quant-ph updates on arXiv.org

Authors: Martin Kliesch, Richard Kueng, Jens Eisert, David Gross

Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancilla systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel’s Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancilla systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case. Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and $\ell_2$-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.