Related papers: Parallel distinguishability of quantum operations
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
Quantum resource theory under different classes of quantum operations advances multiperspective understandings of inherent quantum-mechanical properties, such as quantum coherence and quantum entanglement. We establish hierarchies of…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
The notion of antidistinguishability captures the possibility of ruling out certain alternatives in a quantum experiment without identifying the actual outcome. Although extensively studied for quantum states, the antidistinguishability of…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that…
Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
A non-Hermitean operator does not necessarily have a complete set of eigenstates, contrary to a Hermitean one. An algorithm is presented which allows one to decide whether the eigenstates of a given PT-invariant operator on a…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in details the case of qubit observables. In particular, we show that perfect discrimination with…
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that,…
We prove that the entangling capacity of a two-qubit unitary operator without local ancillas, both with and without the restriction to initial product states, as quantified by the maximum attainable concurrence, is directly related to the…
A bipartite subspace $S$ is called strongly positive-partial-transpose-unextendible (PPT-unextendible) if for every positive integer $k$, there is no PPT operator supporting on the orthogonal complement of $S^{\otimes k}$. We show that a…
It is shown that a quantum controlled-NOT gate simultaneously performs the logical functions of three distinct conditional local operations. Each of these local operations can be verified by measuring a corresponding truth table of four…
We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or…