Transferring elements of a density matrix

Abstract

We study restrictions imposed by quantum mechanics on the process of matrix elements transfer. This problem is at the core of quantum measurements and state transfer. Given two systems $\A$ and $\B$ with initial density matrices $\lambda$ and $r$, respectively, we consider interactions that lead to transferring certain matrix elements of unknown $\lambda$ into those of the final state $\tilde{r}$ of $\B$. We find that this process eliminates the memory on the transferred (or certain other) matrix elements from the final state of $\A$. If one diagonal matrix element is transferred, ${\tilde{r}}_{aa}={\lambda }_{aa}$, the memory on each non-diagonal element ${\lambda }_{a\ne b}$ is completely eliminated from the final density operator of $\A$. Consider the following three quantities $\Re \la_{a\not =b}$, $\Im \la_{a\not =b}$ and $\la_{aa}-\la_{bb}$ (the real and imaginary part of a non-diagonal element and the corresponding difference between diagonal elements). Transferring one of them, e.g., $\Re\tir_{a\not = b}=\Re\la_{a\not = b}$, erases the memory on two others from the final state of $\A$. Generalization of these set-ups to a finite-accuracy transfer brings in a trade-off between the accuracy and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations which account for local aspects of the accuracy-disturbance trade-off in quantum measurements.

9 pages, 2 tables

References in corpus (27)

• Quantum Copying: Beyond the No-Cloning Theorem
• Noncommuting mixed states cannot be broadcast
• Heisenberg's Uncertainty Principle
• Probabilistic cloning and identification of linearly independent quantum states
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Reversible state transfer between light and a single trapped atom
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Impossibility of deleting an unknown quantum state
• Coherent transfer of light polarization to electron spins in a semiconductor
• Constructing Qubits in Physical Systems
• Conservation laws, uncertainty relations, and quantum limits of measurements
• Information transfer and fidelity in quantum copiers
• No-cloning of Orthogonal States in Composite Systems
• Curie-Weiss model of the quantum measurement process
• Quantum state transfer and time-dependent disorder in Quantum Chains
• Superbroadcasting of mixed states
• Entropic information-disturbance tradeoff
• Quantum information storage and state transfer based on spin systems
• Pointer states via Decoherence in a Quantum Measurement
• Towards a unified approach to information-disturbance tradeoffs in quantum measurements
• Information gain versus state disturbance for a single qubit
• Uncertainty characteristics of generalized quantum measurements
• Quantum measurement as driven phase transition: An exactly solvable model
• Quantum measurements without macroscopic superpositions
• Measurement of a Quantum System Coupled to Independent Heat-Bath and Pointer Modes
• The Role of Heat Bath and Pointer Modes in Quantum Measurement
• Cloning of observables

Cited by in corpus (3)

• Understanding quantum measurement from the solution of dynamical models
• Universality of energy conversion efficiency for optimal tight-coupling heat engines and refrigerators
• Information-theoretic limitations on approximate quantum cloning and broadcasting