TY - JOUR A1 - Campbell, Earl T. A1 - Eisert, Jens T1 - Gaussification and entanglement distillation of continuous-variable systems a unifying picture JF - Physical review letters N2 - Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.108.020501 SN - 0031-9007 VL - 108 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Riera, Arnau A1 - Gogolin, Christian A1 - Eisert, Jens T1 - Thermalization in nature and on a quantum computer JF - Physical review letters N2 - In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.108.080402 SN - 0031-9007 VL - 108 IS - 8 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Cubitt, Toby S. A1 - Eisert, Jens A1 - Wolf, Michael M. T1 - The complexity of relating quantum channels to master equations JF - Communications in mathematical physics N2 - Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations. We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description. However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case. Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory. Y1 - 2012 U6 - https://doi.org/10.1007/s00220-011-1402-y SN - 0010-3616 VL - 310 IS - 2 SP - 383 EP - 418 PB - Springer CY - New York ER - TY - JOUR A1 - Mari, Andrea A1 - Eisert, Jens T1 - Positive wigner functions render classical simulation of quantum computation efficient JF - Physical review letters N2 - We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource. Y1 - 2012 U6 - https://doi.org/10.1103/PhysRevLett.109.230503 SN - 0031-9007 VL - 109 IS - 23 PB - American Physical Society CY - College Park ER -