Related papers: Sufficient Conditions and Constraints for Reversin…
A system interacting with its environment will give rise to a quantum evolution. After tracing over the environment the net evolution of the system can be described by a linear Hermitian map. It has recently been shown that a necessary and…
The common wisdom in the field of quantum information theory is that when a system is initially correlated with its environment, the map describing its evolution may fail to be completely positive. If true, this would have practical and…
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
Complete positivity of quantum dynamics is often viewed as a litmus test for physicality, yet it is well known that correlated initial states need not give rise to completely positive evolutions. This observation spurred numerous…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps.…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
Complete positivity is a ubiquitous assumption in the study of quantum systems interacting with the environment, despite repeated efforts to point out that the assumption is not empirically justified. It will be shown that Hamiltonian…
Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We…
We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with…
We investigate the evolution of open quantum systems in the presence of initial correlations with an environment. Here the standard formalism of describing evolution by completely positive trace preserving (CPTP) quantum operations can fail…