相关论文: Commutation relations for arbitrary quantum minors

This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…

It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum…

Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…

We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express…

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field…

Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…

The main theorem of the paper allows to generalize a class of identities among the quantum minors for quantum linear groups to similar identities but with the row labels of the quantum minors involved permuted.

In a recent series of papers we have analyzed a certain deformation of the canonical commutation relations producing an interesting functional structure which has been proved to have some connections with physics, and in particular with…

A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This…

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…

We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…

We show that a set with an action of a locally finite-dimensional free partially commutative monoid and the corresponding semicubical set have isomorpic homology groups. We build a complex of finite length for the computing homology groups…

1. Quantized conductance 2. When 1 mode = 1 atom 3. Photons and Cooper pairs 4. Thermal analogues 5. Shot noise 6. Solid-state electron optics 7. Ultimate confinement 8. Landauer formulas

Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper.…

Quantum simulators hold enormous promise for advancing the modelling of materials and understanding emergent physics, such as high temperature superconductivity and topological order. While correlation functions are, typically,…

Reciprocal pairs of quantum channels are defined as completely positive transformations which admit a rigid, distance-preserving, yet not completely-positive transformation that allows to reproduce the outcome of one from the corresponding…

By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the…