Related papers: Parametrization of quantum states and the quantum …
The quantum Fisher information (QFI) associated with a particular process applied to a many-body quantum system has been suggested as a diagnostic for the nature of the system's quantum state, e.g., a thermal density matrix vs. a pure state…
This thesis deals with General Probabilistic Theories (GPTs) and Entanglement Structures (ESs). An ES is a possible structure of a quantum composite system in GPTs, which is not uniquely determined as the Standard Entanglement Structure…
We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha\beta}(\rho)$…
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…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
Among the surprising features of quantum measurements, the problem of distinguishing and antidistinguishing general quantum measurements is fundamentally appealing. Unlike classical systems, quantum theory offers entangled states and…
The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are {\it particles}, elementary or composite. It follows that each elementary process, hence…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…
Quantum superposition states are behind many of the curious phenomena exhibited by quantum systems, including Bell non-locality, quantum interference, quantum computational speed-up, and the measurement problem. At the same time, many…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We investigate models of nonlinear quantum computation based on deterministic positive trace-preserving (PTP) channels and evolution equations. The models are defined in any finite Hilbert space, but the main results are for dimension $N \!…
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a…
The concept of randomness in quantum computing has been central to construct benchmarking tools, cryptographic protocols, as well as a proof of beyond classical computation. Discerning whether quantum states (or unitaries) are randomly…
The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary…