Abstract
We analyse orthogonal bases in a composite N×N Hilbert space describing a bipartite quantum system and look for a basis with optimal single-sided mutual state distinguishability. This condition implies that in each subsystem the N2 reduced states form a regular simplex of a maximal edge length, defined with respect to the trace distance. In the case N=2 of a two-qubit system our solution coincides with the elegant joint measurement introduced by Gisin. We derive explicit expressions of an analogous constellation for N=3 and provide a general construction of N2 states forming such an optimal basis in HN⊗HN. Our construction is valid for all dimensions for which a symmetric informationally complete (SIC) generalized measurement is known. Furthermore, we show that the one-party measurement that distinguishes the states of an optimal basis of the composite system leads to a local quantum state tomography with a linear reconstruction formula. Finally, we test the introduced tomographical scheme on a complete set of three mutually unbiased bases for a single qubit using two different IBM machines.
Highlights
According to Asher Peres quantum phenomena do not occur in a Hilbert space, they occur in a laboratory [1]
The search for optimal schemes of a quantum measurement applicable for various set-ups is an ongoing task in the field of quantum information
In this work we investigated the question of finding an orthogonal von Neumann measurement for two parties having N levels each, which provides the optimal single-sided distinguishability in terms of singleshot experiments
Summary
According to Asher Peres quantum phenomena do not occur in a Hilbert space, they occur in a laboratory [1]. The vectors used as a tool to compute probabilities describing outcomes of a quantum measurement do live in a complex Hilbert space. The Hilbert space HN is isotropic, ‘all quantum states are equal’. If we consider k = 2 pure quantum states, |φ and |ψ of a fixed finite dimension N , the situation changes, as such a particular pair of states can be characterized by their fidelity, F = | ψ|φ |2. If F = 0 both states are orthogonal, and they are perfectly distinguishable. Some configurations of k quantum states become ‘more equal than the others’
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
