Quantum algorithm for universal implementation of projective measurement of energy

A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by quantum tomography, but the time cost to achieve a given accuracy increases exponentially with the size of the quantum system. In this letter, we improve the time cost by adapting quantum phase estimation, an algorithm designed for computational problems, to measurements on physical systems. We present a PME protocol without quantum tomography for Hamiltonians whose dimension and energy scale are given but otherwise unknown. Our protocol implements a PME to arbitrary accuracy without any dimension dependence on its time cost. We also show that another computational quantum algorithm may be used for efficient estimation of the energy scale. These algorithms show that computational quantum algorithms have applications beyond their original context with suitable modifications.Comment: 4 pages with 9-page supplemental, 4 figures. Comments welcom

Complex conjugation supermap of unitary quantum maps and its universal implementation protocol

A complex conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its complex conjugate $U^*$. First, we present a deterministic quantum protocol that universally implements the complex conjugation supermap when we are given a blackbox quantum circuit, guaranteed to implement some unitary operation, whose only known description is its dimension. We then discuss the complex conjugation supermap in the context of entanglement theory and derive a conjugation-based expression of the $G$-concurrence. Finally, we present a physical process involving identical fermions from which the complex conjugation protocol is derived as a simulation of the process using qudits.Comment: ver.5: published version, 5 pages, 2 figures, double-colum

Quantum computation over the butterfly network

In order to investigate distributed quantum computation under restricted network resources, we introduce a quantum computation task over the butterfly network where both quantum and classical communications are limited. We consider deterministically performing a two-qubit global unitary operation on two unknown inputs given at different nodes, with outputs at two distinct nodes. By using a particular resource setting introduced by M. Hayashi [Phys. Rev. A \textbf{76}, 040301(R) (2007)], which is capable of performing a swap operation by adding two maximally entangled qubits (ebits) between the two input nodes, we show that unitary operations can be performed without adding any entanglement resource, if and only if the unitary operations are locally unitary equivalent to controlled unitary operations. Our protocol is optimal in the sense that the unitary operations cannot be implemented if we relax the specifications of any of the channels. We also construct protocols for performing controlled traceless unitary operations with a 1-ebit resource and for performing global Clifford operations with a 2-ebit resource.Comment: 12 pages, 12 figures, the second version has been significantly expanded, and author ordering changed and the third version is a minor revision of the previous versio

The Cost of Randomness for Converting a Tripartite Quantum State to be Approximately Recoverable

We introduce and analyze a task in which a tripartite quantum state is transformed to an approximately recoverable state by a randomizing operation on one of the three subsystems. We consider cases where the initial state is a tensor product of $n$ copies of a tripartite state $\rho^{ABC}$, and is transformed by a random unitary operation on $A^n$ to another state which is approximately recoverable from its reduced state on $A^nB^n$ (Case 1) or $B^nC^n$ (Case 2). We analyze the minimum cost of randomness per copy required for the task in an asymptotic limit of infinite copies and vanishingly small error of recovery, mainly focusing on the case of pure states. We prove that the minimum cost in Case 1 is equal to the Markovianizing cost of the state, for which a single-letter formula is known. With an additional requirement on the convergence speed of the recovery error, we prove that the minimum cost in Case 2 is also equal to the Markovianizing cost. Our results have an application for distributed quantum computation.Comment: 12 pages, 2 figure