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AIP conference proceedings

General Implementation of All Possible POVMs of Single Photon Polarization States

Sebastian E. Ahnert

Published Jan 1, 2004• 0 citations
Publisher

Abstract

We propose here a single setup for the implementation of all possible positive operator value measurements (POVMs) of a single‐photon polarization state. This includes POVMs with orthogonal projective, non‐orthogonal projective, and non‐projective sets of Kraus operators. Our setup is deterministic as opposed to probabilistic, which means that the setup delivers one of the possible POVM output states in every measurement. Furthermore our method does not require any ancillas except for vacuum states. Finally we illustrate how our setup can be used to implement two well‐known POVMs, including one required for established quantum cryptography protocols [1, 2, 3, 4].

DOI
10.1063/1.1834389

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We propose here a single setup for the implementation of all possible positive operator value measurements (POVMs) of a single‐photon polarization state. This includes POVMs with orthogonal projective, non‐orthogonal projective, and non‐projective sets of Kraus operators. Our setup is deterministic as opposed to probabilistic, which means that the setup delivers one of the possible POVM output states in every measurement. Furthermore our method does not require any ancillas except for vacuum states. Finally we illustrate how our setup can be used to implement two well‐known POVMs, including one required for established quantum cryptography protocols [1, 2, 3, 4].
Positive-operator-value measures (POVM's) are the most general class of quantum measurements. We propose a setup in which all possible POVM's of a single-photon polarization state (corresponding to all possible sets of two-dimensional Kraus operators) can be implemented easily using linear optics elements. This method makes it possible to experimentally realize any projective orthogonal, projective nonorthogonal or nonprojective sets of any number of POVM operators. Furthermore, our implementation only requires vacuum ancillas and is deterministic rather than probabilistic. Thus it realizes every POVM with the correct set of output states. We give the settings required to implement two different well-known nonorthogonal projective POVM's.
Here we propose an implementation of all possible positive-operator-value measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell state measurements, and an entangled three-photon ancilla state, which can be prepared separately and in advance (or ``off-line''). As an example we give the detailed settings for a simultaneous measurement of all four Bell states for an arbitrary two-photon polarization state, which is impossible with linear optics alone.
In this paper we describe a scheme for performing a nonorthogonal projective positive-operator-value measurement of any arbitrary single-photon polarization input state with unit probability of success. While this probability is reached in the limit of infinite cycles of states through the apparatus, only one actual physical setup is required for a feasible implementation. Specifically, our setup implements a set of three nonorthogonal measurement operators at angles of 120\ifmmode^\circ\else\textdegree\fi{} to each other.
Positive-operator-value-measurement (POVM) is one of the essential components of quantum information processing (QIP). Recently a ‘binary measurement tree’ (BST) strategy (PRA 77, 052104) is suggested for implementing arbitrary POVM by sequential two-operator POVMs. We present a simple novel two-operator POVM module via linear optics, which is employed as block to construct a ‘binary measurement tree’ for implementing arbitrary POVM on single photonic polarization qubit. The total complexity of the experimental setup is significantly reduced in contrast to the previous works. As an example, we give the detailed settings of a well-known POVM.
A continuous positive operator-valued measurement (POVM) is described for the polarization state of a single photon propagating in a known spatiotemporal mode. This POVM is shown to be the maximum-likelihood quantum measurement for estimating that polarization state. Moreover, the maximum-likelihood polarization estimate derived from this POVM enables uniformly optimal measure-and-prepare state transmission via classical communication---at the F‾=2/3\overline{F}=2/3F=2/3 classical limit on average teleportation fidelity---for any pure state of polarization. When two continuous-POVM polarimeters are used to detect the singlet state of a pair photons that are in distinct spatial modes, the conditional probability density for one polarimeter's output given the other's encompasses the quantum interference patterns seen in standard singlet-state polarization analysis. For single-photon illumination, a 1:M1:M1:M optical splitter followed by a collection of MMM projective polarization measurements, whose bases are uniformly distributed over the Poincar\'e sphere, yields observation statistics that converge in distribution to those of the continuous-POVM polarimeter as $M\ensuremath{\rightarrow}\ensuremath{\infty}$.
Positive-operator-value measurement (POVM) is the most general class of quantum measurement. We propose a scheme to deterministically implement arbitrary POVMs of single atomic qubit via cavity QED catalysed by only one ancilla atomic qubit. By appropriately entangling two atomic qubits and sequentially measuring the ancilla qubit, any POVM can be implemented step by step. As an application of our scheme, the realization of a specific POVM for optimal unambiguous discrimination (OUD) between two nonorthogonal states is given.