Related papers: Parallel distinguishability of quantum operations
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally…
We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments…
We give a sufficient condition that an operator sum representation of a separable quantum channel in terms of product operators is the unique product representation for that channel, and then provide examples of such channels for any number…
We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular,…
Let $\mathcal{E}$ be a Banach space contained in a Hilbert space $\mathcal{L}$. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambicki\v{\i}, we say that a bounded operator on…
A reasonable quantum information theory for fermions must respect the parity super-selection rule to comply with the special theory of relativity and the no-signaling principle. This rule restricts the possibility of any quantum state to…
A pair of Hermitian operators is canonical if they satisfy the canonical commutation relation. It has been believed that no such canonical pair exists in finite-dimensional Hilbert space. Here, we obtain canonical pairs by noting that the…
Recently, a different form of quantum steering, i.e., certification of quantum steering in a one-sided semi-device-independent way, has been formulated [Jebarathinam \etal Phys. Rev. A 108, 042211 (2023)]. In this work, we use this…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
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…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…
Quantum supermaps are higher-order maps transforming quantum operations into quantum operations. Here we extend the theory of quantum supermaps, originally formulated in the finite dimensional setting, to the case of higher-order maps…
For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak…
We derive finite-dimensional quantum mechanics from a single ontological principle, that \emph{existence is constituted by distinguishability}, together with two structural commitments: finite capacity $N$ (parametric input) and…
We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary…
We examine how to distinguish between unitary operators, when the exact form of the possible operators is not known. Instead we are supplied with "programs" in the form of unitary transforms, which can be used as references for identifying…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…