Related papers: Moments of quantum channel ensembles
The quantification of the quantumness of a quantum ensemble has theoretical and practical significance in quantum information theory. We propose herein a class of measures of the quantumness of quantum ensembles using the unitary similarity…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of…
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science, and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing…
The main purpose of this tutorial is to elucidate in details what should be meant by ensemble of states in quantum mechanics, and to properly address the problem of discriminating, exactly or approximately, two different ensembles. To this…
Quantum theory allows the traversing of multiple channels in a superposition of different orders. When the order in which the channels are traversed is controlled by an auxiliary quantum system, various unknown parameters of the channels…
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…
Collective rotation channels are a fundamental class of channels in quantum computing and quantum information theory. The commutant of the noise operators for such a channel is a C*-algebra which is equal to the set of fixed points for the…
Estimation of channel parameters is important for extending the range and increasing the key rate of continuous variable quantum key distribution protocols. We propose a new estimator for the channel noise parameter based on the method of…
Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information.…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…
State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under…
With rapid progress being made in the development of platforms for quantum computation, there has been considerable interest in whether present-day and near-term devices can be used to solve problems of relevance. A commonly cited…
Entangled multipartite states are resources for universal quantum computation, but they can also give rise to ensembles of unitary transformations, a topic usually studied in the context of random quantum circuits. Using several graph state…
Controlling a large population, in the limit, a continuum, of structurally identical dynamical systems with parametric variations is a pervasive task in diverse applications in science and engineering. However, the severely underactuated…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…