Depicting qudit quantum mechanics and mutually unbiased qudit theories
نویسنده
چکیده
We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.
منابع مشابه
Design of Reversible/Quantum Ternary Multiplexer and Demultiplexer
In this paper, we show realization of macrolevel ternary reversible 2-qudit Feynman gate, 3-qudit controlled Feynman gate, and 3-qudit Toffoli gates using ternary reversible 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates, which are theoretically realizable using quantum technology such as liquid ion trap [10]. Then we show the design of ternary reversible multiplexer and demultiplexer usi...
متن کاملTwelve-dimensional Pauli group contextuality
The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We find that quantum contextuality crops up at dimension twelve in various configurations with a few rays. We use the Shannon capacity for characterizing the co...
متن کاملSeparability criteria via sets of mutually unbiased measurements
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We investigate entanglement detection using sets of MUMs and derive separability criteria for multipartite qudit systems, arbitrary high-dimensional bipartite ...
متن کاملn - qudit state with multipartite entanglement
We propose a protocol Dn for faithfully teleporting an arbitrary n-qudit state with the tensor product state (TPS) of n generalized Bell states (GBSs) as the quantum channel. We also put forward explicit protocol D′ n and D′′ n for faithfully teleporting an arbitrary n-qudit state with two classes of 2n-qudit GESs as the quantum channel, where the GESs are a kind of genuine entangled states we ...
متن کاملCompatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and practical interest. Understanding the invariance of a set of states under certain transformations is mutually associated with a better understanding of some fundamental aspects of quantum mechanics as well as the practical utility of invariant subsystems. For example, DFS/NSs are po...
متن کامل