Related papers: Tests For Complete Positivity of Quantum Channels
Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In…
Network tomography refers to the use of inference techniques for inferring internal network states from end-to-end probes. Quantum probes, implemented by sending blocks of $n$ coherent-state pulses augmented with continuous-variable (CV)…
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…
A recent method to certify the classical capacity of quantum communication channels is applied for general damping channels in finite dimension. The method compares the mutual information obtained by coding on the computational and a…
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and new sequences are ``refuelled'' from a shared provably…
The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state,…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
We introduce two methods for quantum process and detector tomography. In the quantum process tomography method, we develop an analytical procedure for projecting the linear inversion estimation of a quantum channel onto the set of…
We present a protocol for quantum cryptography in which the data obtained for mismatched bases are used in full for the purpose of quantum state tomography. Eavesdropping on the quantum channel is seriously impeded by requiring that the…
A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the…
Quantum capacity quantifies the amount of quantum information that can be transmitted by a quantum channel with an arbitrary small probability of error. Mathematically, the quantum capacity is given by an asymptotic formula involving the…
The Choi-state is an indispensable tool in the study and analysis of quantum channels. Considering a channel in terms of its associated Choi-state can greatly simplify problems. It also offers an alternative approach to the characterisation…
Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel ${\cal E}$, we introduce the concept of its…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
We present an alternative approach to the derivation of benchmarks for quantum channels, such as memory or teleportation channels. Using the concept of effective entanglement and the verification thereof, a testing procedure is derived…
In this report we present a general approach for estimating quantum circuits by means of measurements. We apply the developed general approach for estimating the quality of superconducting and optical quantum chips. Using the methods of…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
A generalized channel is a completely positive map that preserves trace on a given subspace. We find conditions under which a generalized channel with respect to a positively generated subspace J is an extreme point in the set of all such…