Related papers: Absolute dimensionality of quantum ensembles
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
In a predicative framework from basic logic, defined for a model of quantum parallelism by sequents, we characterize a class of first order domains, termed {\em virtual singletons}, which allows a generalization of the notion of duality,…
We present a null witness of the dimension of a quantum system, discriminating real, complex and classical spaces, based on equality due to linear independence. The witness involves only a single measurement with sufficiently many outcomes…
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
Knowing and guessing, these are two essential epistemological pillars in the theory of quantum-mechanical measurement. As formulated quantum mechanics is a statistical theory. In general, a priori unknown states can be completely determined…
Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently-discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles.…
The completeness of quantum state space, is usually expressed as \sum_{m=0}^{\infty}|m><m|=1, where {|m>} is selected set of quantum states (basis). Density matrix |m><m| describes a pure quantum state. In this paper, by virtue of the…
It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the…
Analyzing the dimension of an unknown quantum system in a device-independent manner, i.e., using only the measurement statistics, is a fundamental task in quantum physics and quantum information theory. In this paper, we consider this…
Quantum state elimination measurements tell us what states a quantum system does not have. This is different from state discrimination, where one tries to determine what the state of a quantum system is, rather than what it is not. Apart…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and,…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…