Transformations of Stabilizer States in Quantum Networks

Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC) transformations among stabilizer states. These transformations arise as a physically motivated extension of local operations in quantum networks with access to bipartite entanglement between some of the nodes of the network. First, we show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation, which describes local Clifford transformations among graph states. Then, we introduce a mathematical framework to study PLC equivalence of stabilizer states, relating it to the classification of tuples of bilinear forms. This framework allows us to study decompositions of stabilizer states into tensor products of indecomposable ones, that is, decompositions into states from the entanglement generating set (EGS). While the EGS is finite up to $3$ parties [Bravyi et al., J. Math. Phys. {\bf 47}, 062106~(2006)], we show that for $4$ and more parties it is an infinite set, even when considering party-local unitary transformations. Moreover, we explicitly compute the EGS for $4$ parties up to $10$ qubits. Finally, we generalize the framework to qudit stabilizer states in prime dimensions not equal to $2$, which allows us to show that the decomposition of qudit stabilizer states into states from the EGS is unique.Comment: 37 pages, 7 figures, final versio

Indistinguishability of identical bosons from a quantum information theory perspective

Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on additional assumptions on the input state of the interferometer, such as, for instance, a fixed mode occupation, nor on any assumption on the degrees of freedom that potentially make the particles distinguishable. We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability, and derive tight lower bounds on it that can be efficiently measured in experiments. Moreover, we present a consistent definition of perfect distinguishability and characterize the corresponding set of states. In particular, we show that these states are diagonal in the computational basis up to a permutationally invariant unitary. Moreover, we find that convex combinations of states that describe partially distinguishable and perfectly indistinguishable particles can lead to perfect distinguishability, which itself is not preserved under convex combinations

Measurement outcomes that do not occur and their role in entanglement transformations

The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for both theoretical and practical reasons. As LOCC has a highly intricate structure, sometimes the larger set of separable (SEP) maps is considered, which has a mathematically much simpler description. In the literature, mainly SEP maps consisting of invertible Kraus operators have been taken into account. In this paper we show that the consideration of those maps is not sufficient when deciding whether a state can be mapped to another via general SEP transformations. This is done by providing explicit examples of transformations among pure three- and five-qubit states, which are feasible via SEP maps containing singular Kraus operators, however, not possible via SEP maps containing solely regular Kraus operators. The key point that allows to construct the SEP maps is to introduce projective measurements that occur with probability zero on the input state. The fact that it is not sufficient to consider SEP maps composed out of regular Kraus operators even in the case of pure state transformations, also affects the results on LOCC transformations among pure states. However, we show that non-invertible Kraus operators do not help in state transformations under LOCC with finitely many rounds of classical communication, i.e. the necessary and sufficient condition for SEP transformations with invertible Kraus operators is still a necessary condition for convertibility under finite-round LOCC. Moreover, we show that the results on transformations via SEP that are not possible with LOCC (including infinitely many rounds of classical communication) presented in Hebenstreit et al 2016 Phys. Rev. A 93, 012339 are not affected.BK thanks R Brieger and D Sauerwein for discussions related to the characterization of the local unitary symmetries of special graph states. ME, MH, and BK acknowledge financial support from the Austrian Science Fund (FWF) grant DK-ALM: W1259-N27 and the SFB BeyondC (Grant No. F7107). Furthermore, ME and BK acknowledge support of the Austrian Academy of Sciences via the Innovation Fund 'Research, Science and Society' as well as support from the Austrian Science Fund (FWF) grant FG5-L. CS acknowledges support by the Austrian Science Fund (FWF): J 4258-N27 and the ERC (Consolidator Grant 683107/TempoQ). JIdV acknowledges financial support by the Spanish MINECO through Grants MTM2017-84098-P and MTM2017-88385-P and by the Comunidad de Madrid through Grant QUITEMAD-CM P2018/TCS-4342

Optimization and performance study of a proton CT system for pre-clinical small animal imaging

Proton computed tomography (pCT) promises to reduce or even eliminate range uncertainties inherent in the conversion of Hounsfield units into relative stopping power (RSP) for proton therapy treatment planning. This is of particular interest for proton irradiation studies in animal models due to the high precision required and uncertainties in tissue properties. We propose a dedicated single-particle tracking pCT system consisting of low material budget floating strips Micromegas detectors for tracking and a segmented time-projection-chamber with vertical Mylar absorbers, functioning as a range telescope. Based on Monte Carlo simulations of a realistic in silico beam and detector implementation, a geometrical optimization of the system components was conducted to safeguard an ideal operation close to intrinsic performance limits at 75 MeV. Moreover, the overall imaging capabilities relevant for pre-clinical proton therapy treatment planning were evaluated for a mouse model. In order to minimize extrinsic uncertainties in the estimated proton trajectories, a spacing of the two tracking planes of at least 7 cm is required in both tracking detectors. Additionally, novel in-house developed and produced aluminum-based readout electrodes promise superior performance with around 3mm-1 spatial resolution due to the reduced material budget. Concerning the range telescope, an absorber thickness within 500 µm to 750 µm was found to yield the best compromise between water-equivalent path length resolution and complexity of the detector instrumentation, still providing sub-0.5% RSP accuracy. The optimized detector configuration enables better than 2% range accuracy for proton therapy treatment planning in pre-clinical data sets. This work outlines the potential of pCT for small animal imaging. The performance of the proposed and optimized system provides superior treatment planning accuracy compared to conventional X-ray CT. Thus, pCT can play an important role in translational and pre-clinical cancer research