Related papers: Optimality Condition for the Petz Map
To establish an entangled state of optimal fidelity between two distant observers when the available quantum channel is noisy, is a central problem in quantum information theory. We consider an instance of this problem for two-qubit systems…
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…
This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013)] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random…
An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the…
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the…
The entanglement of formation gives a necessary and sufficient condition for the existence of a perfect quantum error correction procedure.
We investigate the quantum information reclaim from the environment after amplitude damping has occurred. In particular we address the question of optimal measurement on the environment to perform the best possible correction on two and…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting…
The Petz recovery map (1986) provably reverses a noisy quantum channel on a reference state, but its algorithmic relevance to real, dissipation-dominated platforms has remained unclear. Using the open-source \texttt{organic-qc-bench}…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and…
Near-term quantum computations are limited by high error rates, the scarcity of qubits and low qubit connectivity. Increasing support for mid-circuit measurements and qubit reset in near-term quantum computers enables qubit reuse that may…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
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 constrained $\ell_p^p/\ell_q^p$ ratio model is scale invariant and is therefore attractive for sparse signal recovery. However, its nonconvex, nonsmooth, and fractional structure makes a unified theoretical and algorithmic analysis…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of minimal sufficient Jordan algebras, which can be seen to…