Picturing qubits in phase space
نویسنده
چکیده
Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function—a generalized Wigner function—on a discrete 2 × 2 phase space. The phase space is based on the finite field having 2 elements, and its geometric structure leads naturally to the construction of a complete set of 2 + 1 mutually conjugate bases. PACS numbers: 03.65.Ca, 03.65.Ta, 03.65.Wj, 02.10.De
منابع مشابه
ar X iv : 0 80 6 . 07 26 v 1 [ qu an t - ph ] 4 J un 2 00 8 Mutually unbiased bases in discrete phase space
We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(2n) and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide...
متن کاملDiscrete Coherent States for N Qubits
Received Day Month Year Revised Day Month Year Discrete coherent states for a system of n qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function.
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 کاملPhase-space Representation for Qubits
Problems involving interacting spins or qubits are often regarded as computationally intractable. These are frequently considered as only being accessible using quantum computers, which are not yet developed. At the same time, there is a ‘chicken and egg’ problem: it is difficult to design a quantum computer with no effective means to simulate its behaviour, including inevitable sources of loss...
متن کاملar X iv : 0 70 4 . 12 77 v 1 [ qu an t - ph ] 1 0 A pr 2 00 7 DISCRETE PHASE SPACE AND MINIMUM - UNCERTAINTY STATES
The quantum state of a system of n qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in the finite field F 2 n. Within this framework, we show that one can make sense of the notion of a " rotationally invariant state " of any collection of qubits, and that any such state is, in a well defined sense, a state of minimum uncertainty.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IBM Journal of Research and Development
دوره 48 شماره
صفحات -
تاریخ انتشار 2004