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arXiv:quant-ph/0504222 · Journal of Physics A Mathematical and General

Concurrence classes for an arbitrary multi-qubit state based on a positive operator valued measure

Hoshang Heydari

Published Nov 30, 2005• 5 citations
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Abstract

In this paper, we propose concurrence classes for an arbitrary multi-qubit state based on orthogonal complement of a positive operator valued measure, or POVM for short, on quantum phase. In particular, we construct concurrence for an arbitrary two-qubit state and concurrence classes for the three- and four-qubit states. Finally, we construct W m and GHZ m class concurrences for multi-qubit states. The unique structure of our POVM enables us to distinguish different concurrence classes for multi-qubit states.

DOI
10.1088/0305-4470/38/50/009

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In this paper, we propose concurrence classes for an arbitrary multi-qubit state based on orthogonal complement of a positive operator valued measure, or POVM for short, on quantum phase. In particular, we construct concurrence for an arbitrary two-qubit state and concurrence classes for the three- and four-qubit states. Finally, we construct W m and GHZ m class concurrences for multi-qubit states. The unique structure of our POVM enables us to distinguish different concurrence classes for multi-qubit states.
In this paper, we will define concurrence classes for a general multipartite state based on an orthogonal complement of a positive operator valued measure on quantum phase. In particular, we will define concurrence for an arbitrary bipartite state and concurrence classes for the three- and four-partite states. And finally, we will define concurrence for WmW^{m}Wm and GHZmGHZ^{m}GHZm classes of a general multipartite state.
We construct quantum gate entanglers for different classes of multipartite states based on definition of W and GHZ concurrence classes. First, we review the basic construction of concurrence classes based on orthogonal complement of a positive operator valued measure (POVM) on quantum phase. Then, we construct quantum gates entanglers for different classes of multi-qubit states. In particular, we show that these operators can entangle multipartite state if they satisfy some conditions for W and GHZ classes of states. Finally, we explicitly give the W class and GHZ classes of quantum gate entanglers for four-qubit states.
We propose a entanglement generating set for a general multipartite state based on the of concurrence. In particular, we show that concurrence for general multipartite states can be constructed by different classes of local operators which are defined by complement of positive operator valued measure on quantum phases. The entanglement generating set consists of different classes of entanglement that are detected by these classes of operators and contributes to the degree of entanglement for a general multipartite state.
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.
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.