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arXiv:quant-ph/0202152 · Physical Review Letters

Universal Measurement Apparatus Controlled by Quantum Software

Jaromı́r Fiurášek, Miloslav Dušek, Radim Filip

Published Oct 16, 2002• 63 citations
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Abstract

We propose a quantum device that can approximate any projective measurement on a qubit-a quantum "multimeter." The desired measurement basis is selected by the quantum state of a "program register." Two different kinds of programs are considered and in both cases the device is optimized with respect to maximal average fidelity (assuming uniform distribution of measurement bases). Quantum multimeters exhibiting the covariance property are introduced and an optimal covariant multimeter with a single-qubit program register is found. Possible experimental realization of the simplest proposed device is presented.

DOI
10.1103/physrevlett.89.190401

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We propose a quantum device that can approximate any projective measurement on a qubit-a quantum "multimeter." The desired measurement basis is selected by the quantum state of a "program register." Two different kinds of programs are considered and in both cases the device is optimized with respect to maximal average fidelity (assuming uniform distribution of measurement bases). Quantum multimeters exhibiting the covariance property are introduced and an optimal covariant multimeter with a single-qubit program register is found. Possible experimental realization of the simplest proposed device is presented.
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states and then the universal multimeters for a special choice of program. In both cases we start with deterministic but error-prone devices and then proceed to devices that never make a mistake but from time to time give an inconclusive result. These multimeters are optimized (for a given type of program) with respect to the minimum probability of an inconclusive result. This concept is further generalized to multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.
We review some partial results for two strictly related problems. The first problem consists in finding the optimal joint unitary transformation on system and ancilla which is the most efficient in programming any desired channel on the system by changing the state of the ancilla. In this respect we present a solution for dimension two for both system and ancilla. The second problem consists in finding the optimal universal programmable detector, namely a device that can be tuned to perform any desired measurement on a given quantum system, by changing the state of an ancilla. With a finite dimension for the ancilla only approximate universal programmability is possible, with minimal dimension increasing function versus the precision of the approximation. We show that one can achieve a dimension growing polynomially versus the precision, and even linearly in specific cases.
We propose a ``programmable'' quantum device that is able to perform a specific generalized measurement from a certain set of measurements depending on a quantum state of a ``program register.'' In particular, we study a situation when the programmable measurement device serves for the unambiguous discrimination between nonorthogonal states. The particular pair of states that can be unambiguously discriminated is specified by the state of a program qubit. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subsets it can be very close to the optimal value.
We consider a device which can be programed using coherent states of light to approximate a given projective measurement on an input coherent state. We provide and discuss three practical implementations of this programmable projective measurement device with linear optics, involving only balanced beam splitters and single photon threshold detectors. The three schemes optimally approximate any projective measurement onto a program coherent state. We further extend these to the case where there are no assumptions on the input state. In this setting, we show that our scheme enables an efficient verification of an unbounded untrusted source with only local coherent states, balanced beam splitters, and threshold detectors. Exploiting the link between programmable measurements and generalized swap test, we show as a direct application that our schemes provide an asymptotically quadratic improvement in existing quantum fingerprinting protocol to approximate the Euclidean distance between two unit vectors.
We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers, and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with some probability of success, tell us whether the unknown state in the data register matches the state stored in the first or the second program register. We show that the optimal device, i.e., the one that maximizes the probability of success, is universal. It does not depend on the actual unknown states that we wish to discriminate.