Related papers: Trace distance from the viewpoint of quantum opera…
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures.…
The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how…
The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable…
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
We investigate the quantum phase transitions of spin systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration examples, a…
It is claimed in the many papers that a trace distance ($d$) guarantees the universal composition security in quantum key distribution (QKD). In this introduction paper, at first, it is explicitly explained what is the main misconception in…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
Continuous-variable quantum systems are central to quantum technologies, with Gaussian states playing a key role due to their broad applicability and simple description via first and second moments. Distinguishing Gaussian states requires…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one…
Recently, a measure for the non-Markovian behavior of quantum processes in open systems has been developed which is based on the quantification of the flow of information between the open system and its environment [Phys. Rev. Lett. 103,…
We present a system to measure the distance between two parties that allows only trusted people to access the result. The security of the protocol is guaranteed by the complementarity principle in quantum mechanics. The protocol can be…
The effect of quantum steering describes a possible action at a distance via local measurements. In the last few years, several criteria have been proposed to detect this type of correlation in quantum systems. However, there are few…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
Transforming an initial quantum state into a target state through the fastest possible route---a quantum brachistochrone---is a fundamental challenge for many technologies based on quantum mechanics. Here, we demonstrate fast coherent…
We investigate the speed limit of the state transformation in open quantum systems described by the Lindblad type quantum master equation. We obtain universal bounds of the total entropy production described by the trace distance between…
Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace distance of coherence on pure states. Our…
We define and analyze measures of correlations for bipartite states based on trace distance. For Bell diagonal states of two qubits, in addition to the known expression for quantum correlations using this metric, we provide analytic…