Engineering topics

Grassl, Markus

Publications and source records attributed to Grassl, Markus.

3 records

DOE OSTI2014

Canonical form of three-fermion pure-states with six single particle states

We construct a canonical form for pure states in Λ³(C⁶), the three-fermion system with six single particle states, under local unitary (LU) transformations, i.e., the unitary group U(6). We also construct a minimal set of generators of the algebra of polynomial U(6)-invariants on Λ³(C⁶). It turns out that this algebra is isomorphic to the algebra of polynomial LU-invariants of three-qubits which are additionally invariant under qubit permutations. As a consequence of this surprising fact, we deduce that there is a one-to-one correspondence between the U(6)-orbits of pure three-fermion states in Λ³(C⁶) and the LU orbits of pure three-qubit states when qubit permutations are allowed. As an important byproduct, we obtain a new canonical form for pure three-qubit states under LU transformations U(2) × U(2) × U(2) (no qubit permutations allowed)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Quantum-capacity-approaching codes for the detected-jump channel

The quantum-channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity-approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Structured error recovery for code-word-stabilized quantum codes

Code-word-stabilized (CWS) codes are, in general, nonadditive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical nonlinear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less and employs a separate n-qubit measurement in each test. In this article, we suggest an error grouping technique that allows one to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3{sup t} times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗