Related papers: Antidistinguishability of Pure Quantum States
We study the problem of discriminating between non-orthogonal quantum states with least probability of error. We demonstrate that this problem can be simplified if we solve for the error itself rather than solving directly for the optimal…
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states {\rho} with the property that U^*{\rho}U is separable for all unitary matrices U. This problem has been solved when the…
For multipartite states we consider a notion of D-symmetry. For a system of $N$ qubits it concides with usual permutational symmetry. In case of $N$ qudits ($d\geq 3$) the D-symmetry is stronger than the permutational one. For the space of…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measure defined by…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where $\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the positive weights…
The reduction criterion is a well known necessary condition for separable states, and states violating this condition are entangled and also 1-distillable. In this paper we introduce a new set of necessary conditions for separability of…
Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
In this article, we study an opposite problem of universal quantum state comparison, that is unambiguous determining whether multiple unknown quantum states from a Hilbert space are orthogonal or not. We show that no unambiguous quantum…
In this article, we show a sufficient and necessary condition for locally distinguishable bipartite states via one-way local operations and classical communication (LOCC). With this condition, we present some minimal structures of one-way…
In this paper, we study the separability of quantum states in bosonic system. Our main tool here is the "separability witnesses", and a connection between "separability witnesses" and a new kind of positivity of matrices--- "Power Positive…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for…
Finding the least measurement settings to determine an arbitrary pure state has been long known as the Pauli problem. In the fixed measurement scheme four orthonormal bases are required even though there are far less parameters in a pure…
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states.…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…