Related papers: On Estimating the State of a Finite Level Quantum …
Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
The unitarity of quantum evolutions implies that the overlap between two initial states does not change in time. This property is commonly believed to explain the lack of state sensitivity in quantum theory, a feature that is prevailing in…
We suggest solving the measurement problem by postulating the existence of a special future final boundary condition for the universe. Although this is an extension of the way boundary conditions are usually chosen (in terrestrial…
We analyze the complexity of learning $n$-qubit quantum phase states. A degree-$d$ phase state is defined as a superposition of all $2^n$ basis vectors $x$ with amplitudes proportional to $(-1)^{f(x)}$, where $f$ is a degree-$d$ Boolean…
In this contribution we group the operator basis for d^2 dimensional Hilbert space in a way that enables us to relate bases of entangled states with single particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
In this paper we investigate repeated weak measurements,without post-selection, on a \emph{single copy} of an \emph{unknown} quantum state. The resulting random walk in state space is precisely characterised in terms of joint probabilities…
We consider the problem of correctly classifying a given quantum two-level system (qubit) which is known to be in one of two equally probable quantum states. We assume that this task should be performed by a quantum machine which does not…
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent…
The well-known algorithm for quantum phase estimation requires that the considered unitary is available as a conditional transformation depending on the quantum state of an ancilla register. We present an algorithm converting an unknown…
Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
State of a $d$-dimensional quantum system can only be inferred by performing an informationally complete measurement with $m\geqslant d^2$ outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…