Remarks on Duality Transformations and Generalized Stabilizer States

We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well as exact characterizations of ground states employing non-Hermitean eigenvalue equations and use this to motivate a generalization of the stabilizer formalism to non-Hermitean operators. The resulting class of states is larger than that of standard stabilizer states and allows for example for continuous variation of local entropies rather than the discrete values taken on stabilizer states and the exact description of certain ground states of Hamilton operators.Comment: Contribution to Special Issue in Journal of Modern Optics celebrating the 60th birthday of Peter Knigh

Quantum data processing and error correction

This paper investigates properties of noisy quantum information channels. We define a new quantity called {\em coherent information} which measures the amount of quantum information conveyed in the noisy channel. This quantity can never be increased by quantum information processing, and it yields a simple necessary and sufficient condition for the existence of perfect quantum error correction.Comment: LaTeX, 20 page

Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em e.g.} near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transfrom one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D(M)$ of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$, showing $D(M)>0$ if \bra{\Psi^-}M\ket{\Psi^-}>\half.Comment: 4 pages (revtex) plus 1 figure (postscript). See also http://vesta.physics.ucla.edu/~smolin/ . Replaced to correct interchanged $\sigma_x$ and $\sigma_z$ near top of column 2, page

Strengthened Lindblad inequality: applications in non equilibrium thermodynamics and quantum information theory

A strengthened Lindblad inequality has been proved. We have applied this result for proving a generalized $H$-theorem in non equilibrium thermodynamics. Information processing also can be considered as some thermodynamic process. From this point of view we have proved a strengthened data processing inequality in quantum information theory.Comment: 7 pages, revte

Simple Realization Of The Fredkin Gate Using A Series Of Two-body Operators

The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.Comment: Revtex 3.0, 7 pages, 3 figures appended at the end, please refer to the comment lines at the beginning of the manuscript for reasons of replacemen

Time-convolutionless reduced-density-operator theory of a noisy quantum channel: a two-bit quantum gate for quantum information processing

An exact reduced-density-operator for the output quantum states in time-convolutionless form was derived by solving the quantum Liouville equation which governs the dynamics of a noisy quantum channel by using a projection operator method and both advanced and retarded propagators in time. The formalism developed in this work is general enough to model a noisy quantum channel provided specific forms of the Hamiltonians for the system, reservoir, and the mutual interaction between the system and the reservoir are given. Then, we apply the formulation to model a two-bit quantum gate composed of coupled spin systems in which the Heisenberg coupling is controlled by the tunneling barrier between neighboring quantum dots. Gate Characteristics including the entropy, fidelity, and purity are calculated numerically for both mixed and entangled initial states

Building multiparticle states with teleportation

We describe a protocol which can be used to generate any N-partite pure quantum state using Einstein-Podolsky-Rosen (EPR) pairs. This protocol employs only local operations and classical communication between the N parties (N-LOCC). In particular, we rely on quantum data compression and teleportation to create the desired state. This protocol can be used to obtain upper bounds for the bipartite entanglement of formation of an arbitrary N-partite pure state, in the asymptotic limit of many copies. We apply it to a few multipartite states of interest, showing that in some cases it is not optimal. Generalizations of the protocol are developed which are optimal for some of the examples we consider, but which may still be inefficient for arbitrary states.Comment: 11 pages, 1 figure. Version 2 contains an example for which protocol P3 is better than protocol P2. Correction to references in version

A Note on Invariants and Entanglements

The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential applications in studying separability and calculating entanglement of formation for high dimensional mixed quantum states.Comment: Latex, 11 page

Simple Quantum Error Correcting Codes

Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where C_1 and C_2 are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C_1 to have reduced distance, and introducing sign changes among the code words in a systematic manner. This systematic approach leads to single-error correcting codes for 3, 4 and 5 information qubits with block lengths of 8, 10 and 11 qubits respectively.Comment: Submitted to Phys. Rev. A. in May 1996. 21 pages, no figures. Further information at http://eve.physics.ox.ac.uk/ASGhome.htm