Related papers: `Lazy' quantum ensembles
In this note I will present a subtle interplay between density matrices and the knowledge about their preparation, and I will argue that there is a need to consider a new type of quantum state, in between pure states and density matrices.
Suppose two distant observers Alice and Bob share a pure biparticle entangled state secretly chosen from a set, it is shown that Alice (Bob) can probabilistic concentrate the state to a maximally entangled state by applying local operations…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
The unknown state $\hrho$ of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix $\hrho$ and the…
The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time. In the classical case, it is well known that the optimal strategy trivially consists of querying the…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic on which they…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the…
There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper we focus on preparing arbitrary spin eigenstates whose subset contain important…
We consider an unknown quantum state shared between two parties, Alice and Bob, and ask how much quantum communication is needed to transfer the full state to Bob. This problem is known as state merging and was introduced in [Horodecki et…
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later…
The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state…
We introduce a batched lazy algorithm for supervised classification using decision trees. It avoids unnecessary visits to irrelevant nodes when it is used to make predictions with either eagerly or lazily trained decision trees. A set of…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…