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Chinese Physics Letters

Simple Linear Optical ‘Binary Measurement Tree’ for Single Photonic Polarization Qubit

Han Yang, Wei Wu, Chun-Wang Wu, Ping‐Xing Chen, Cheng-Zu Li

Published Feb 1, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/26/2/020311

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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.
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.
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.
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].
We report an experimental implementation of a single-qubit generalized measurement scenario, the positive-operator valued measure (POVM), based on a quantum walk model. The qubit is encoded in a single-photon polarization. The photon performs a quantum walk on an array of optical elements, where the polarization-dependent translation is performed via birefringent beam displacers and a change of the polarization is implemented with the help of wave plates. We implement: (i) trine POVM, i.e., the POVM elements uniformly distributed on an equatorial plane of the Bloch sphere; (ii) symmetric-informationally-complete (SIC) POVM; and (iii) unambiguous discrimination of two nonorthogonal qubit states.
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state tomography and for preparing arbitrary mixed states.
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.