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AIP conference proceedings

Circuits for Distributing Quantum Measurement

Prasanta Kumar Panigrahi, Manish K. Gupta, Anirban Pathak, R. Srikanth

Published Jan 1, 2006• 10 citations
Publisher

Abstract

We provide explicit quantum circuits for the distributed measurement of Bell states in the Hilbert space Cdn, where d is qudit dimension. We discuss a method for generalizing this to distributed measurements on any set of orthogonal states distributed among n parties. From the practical viewpoint, we show that such distributed measurements can help lower quantum communication complexity under certain conditions.

DOI
10.1063/1.2400891

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We provide explicit quantum circuits for the distributed measurement of Bell states in the Hilbert space Cdn, where d is qudit dimension. We discuss a method for generalizing this to distributed measurements on any set of orthogonal states distributed among n parties. From the practical viewpoint, we show that such distributed measurements can help lower quantum communication complexity under certain conditions.
A question of theoretical and practical interest is how a quantum system may be measured indirectly by means of an ancilla that interacts with it, and furthermore, how a system of ancillas may be used to implement a coherent measurement of spatially separated qudits. We provide general circuits that can be used to implement such measurements. These circuits are relevant to quantum error correction, measurement-based quantum computation and Bell state discrimination across a quantum network involving multiple parties. The last mentioned problem is treated in detail. Our circuitry can also help to optimize the quantum communication complexity for performing measurements in distributed quantum computing.
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We provide explicit quantum circuits for the non-destructive deterministic discrimination of Bell states in the Hilbert space CdnC^{d^{n}}Cdn, where ddd is qudit dimension. We discuss a method for generalizing this to non-destructive measurements on any set of orthogonal states distributed among nnn parties. From the practical viewpoint, we show that such non-destructive measurements can help lower quantum communication complexity under certain conditions.
A quantum protocol for sharing an arbitrary two-qubit state between N parties is introduced. Any of the members, can retrieve the state, only with collaboration of the other parties. We will show that in terms of resources, i.e. the number of classical bits, the number of Bell pairs shared, and also the type of measurements, our protocol is more efficient. For achieving this, we introduce the basic technique of secure passing of an unknown two qubit state among a sequence of parties, none of which can retrieve the state without authorization of the sender and the other members of the group.
Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This work proposes suitable quantum probes to reduce measurements in distributed sub-systems. Probes are introduced in the context of distributed Grover search. These are shown to be indeed efficient. The latter can be generalized to be applicable to other distributed algorithms of interest.
Focus is on two parties with Hilbert spaces of dimension d, i.e. "qudits". In the state space of these two possibly entangled qudits an analogue to the well known tetrahedron with the four qubit Bell states at the vertices is presented. The simplex analogue to this magic tetrahedron includes mixed states. Each of these states appears to each of the two parties as the maximally mixed state. Some studies on these states are performed, and special elements of this set are identified. A large number of them is included in the chosen simplex which fits exactly into conditions needed for teleportation and other applications. Its rich symmetry - related to that of a classical phase space - helps to study entanglement, to construct witnesses and perform partial transpositions. This simplex has been explored in details for d=3. In this paper the mathematical background and extensions to arbitrary dimensions are analysed.