Related papers: Relation Between Quantum Speed Limits And Metrics …
A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and…
Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy)…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. The resulting \textit{quantum measure} $\mu$ is defined for arbitrary events (sets…
Parallels between the notions of nonlinear pseudobosons and of an apparent non-Hermiticity of observables as shown in paper I (arXiv: 1109.0605) are demonstrated to survive the transition to the quantum models based on the use of unbounded…
We present a simple derivation of the formula for the Hamiltonian operator(s) that achieve the fastest possible unitary evolution between given initial and final states. We discuss how this formula is modified in pseudo-Hermitian quantum…
The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…
We introduce a single-number metric, quantum volume, that can be measured using a concrete protocol on near-term quantum computers of modest size ($n\lesssim 50$), and measure it on several state-of-the-art transmon devices, finding values…
The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed…
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a…
Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
Quantum speed limits are usually regarded as fundamental restrictions, constraining the amount of computation that can be achieved within some given time and energy. Complementary to this intuition, here we show that these limitations are…
Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the…
In the Schr{\"o}dinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture…