Discrete Wigner functions and quantum computational speed-up
نویسنده
چکیده
In quant-ph/0401155 Wootters and colaborators defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set Cd of states having non-negative W simultaneously in all definitions of W in this class. For d ≤ 5 I show Cd is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speed-up in pure-state quantum computation.
منابع مشابه
A Wigner distribution function for finite oscillator systems
We define a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum. The distribution function is thus defined on discrete phase-space, i.e. on a finite discrete square grid. These discrete Wigner functions possess a number of properties similar to the Wigner function for a continuous quant...
متن کاملDiscrete phase-space structures and Wigner functions for N qubits
We further elaborate on a phase-space picture for a system of N qubits and explore the structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves satisfying certain additional properties and different entanglement properties. We discuss the construction of discrete covariant Wigner functions for these bundles and provide several illuminating examples.
متن کاملInterference in discrete Wigner functions
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We consider “cat” states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete...
متن کاملPositive Wigner functions render classical simulation of quantum computation efficient.
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 ope...
متن کاملnt - p h / 01 06 10 9 v 2 2 5 Ju n 20 01 Wigner - function description of quantum teleportation in arbitrary dimensions and continuous limit
We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the telepor-tation protocol. In addition within the framework of the Wigner-function formalism all the imperfections of the manipulations can be easily taken into account. All quantum mechanical ph...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004