Related papers: Approximating quantum channels by completely posit…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
If $H_1$ and $H_2$ are finite-dimensional Hilbert spaces, a channel from $H_1$ to $H_2$ is a completely positive, linear map $\mathcal{I}$ that takes the set of states $\mathcal{S}(H_1)$ for $H_1$ to the set of states $\mathcal{S}(H_2)$ for…
Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of…
We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the incorporation of prior knowledge of the class…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…
The fragile nature of quantum information makes it practically impossible to completely isolate a quantum state from noise under quantum channel transmissions. Quantum networks are complex systems formed by the interconnection of quantum…
Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
Quantum coherence is a fundamental property that can emerge within any quantum system. Incoherent operations, defined in terms of the Kraus decomposition, take an important role in state transformation. The maximum number of incoherent…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging valuable open problem in quantum information theory. Here we introduce a systematic approach that…
A method to optimize the cost of a quantum channel is developed. The goal is to determine the cheapest channel that produces prescribed output states for a given set of input states. This is essentially a quantum version of optimal…
Determining whether a noisy quantum channel can be used to reliably transmit quantum information at a non-zero rate is a challenging problem in quantum information theory. This is because it requires computation of the channel's coherent…
We consider a quantum version of the famous low-rank approximation problem. Specifically, we consider the distance $D(\rho,\sigma)$ between two normalized quantum states, $\rho$ and $\sigma$, where the rank of $\sigma$ is constrained to be…
We demonstrate that the control protocols of quantum information devices can be simulated by assuming a low-rank ansatz for the density matrix. The rationale underlying this assumption is that quantum information protocols, by design,…
There are a few obstacles, which bring about imperfect quantum teleportation of a continuous variable state, such as unavailability of maximally entangled two-mode squeezed states, inefficient detection and imperfect unitary transformation…
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a two-dimensional Hilbert space in which each party's space is…