Related papers: Geometric interpretation for A-fidelity and its re…
We relate gate fidelities of experimentally realized quantum operations to the broadcasting property of their ideal operations, and show that the more parties a given quantum operation can broadcast to, the higher gate fidelities of its…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
A bipartite quantum state is tomographically faithful when it can be used as an input of a quantum operation acting on one of the two quantum systems, such that the joint output state carries a complete information about the operation…
In this work, we present a geometrical formulation of quantum thermodynamics based on contact geometry and principal fiber bundles. The quantum thermodynamic state space is modeled as a contact manifold, with equilibrium Gibbs states…
We present a derivation and numerous applications of a compact explicit formula for the average fidelity of a quantum operation on a finite dimensional quantum system. The formula can be applied to averages over particularly relevant…
For the eight-dimensional Riemannian manifold comprised by the three-level quantum systems endowed with the Bures metric, we numerically approximate the integrals over the manifold of several functions of the curvature and of its…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
We present a general theoretical formalism to compute the fidelity of transformations of unknown quantum states. We then focus on the case of Gaussian transformations of continuous variable quantum systems, where, for the case of a Gaussian…
In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find…
To certify that an experimentally implemented quantum transformation is a certain unitary operation U on a d-dimensional Hilbert space, it suffices to determine fidelities of output states for d+1 suitably chosen pure input states [Reich et…
Verifying the proper preparation of quantum states is essential in modern quantum information science. Various protocols have been developed to estimate the fidelity of quantum states produced by different parties. Direct fidelity…
The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it allows to derive the ultimate bounds of the achievable precision. We show a relation between the statistical distance…
We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
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…
The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a…
Quantum technology has led to increasingly sophisticated and complex quantum devices. Assessing their reliability (quantum reliability) is an important issue. Although reliability theory for classical devices has been well developed in…
The quantum geometry in the momentum space of semiconductors and insulators, described by the quantum metric of the valence band Bloch state, has been an intriguing issue owing to its connection to various material properties. Because the…