### Entanglement and One-Way Quantum Computing

**Prof. Anton Zeilinger [photo credit: Jacqueline Godany]**

**Authors:**

**Robert Prevedel**

**and**

**Anton Zeilinger**

Affiliation:

Affiliation:

**Faculty of Physics, University of Vienna**

and

**Institute of Quantum Optics and Quantum Information,**

**Austrian Academy of Science**

**.**

[This is an invited article based on some recent publications by the authors in various journals referred below.

-- 2Physics.com Team]

According to Erwin Schrödinger [1], one of the founding fathers of quantum mechanics, entanglement is the essence of quantum physics. It inspires fundamental questions about the principles of nature and is also the basis for emerging technologies [2] of quantum information processing such as quantum cryptography [3], quantum teleportation [4,5] and quantum computation [6].

Entangled particles possess correlations stronger than those allowed by classical physics, and can only be described by their joint behaviour, no matter how far the two particles are located from each other. Imagine two ‘entangled coins’, placed at opposite ends of a galaxy, each of which, when thrown individually, yields a random results (head or tails). However, owing to entanglement between the coins, the throw of the second coin always leads to an outcome that is fully determined by the result of rolling the first one, independent of their spatial separation or the time ordering of the throws.

This feature can be used to transmit information securely between two parties (quantum cryptography) or, when generalized to many particles, to process information faster and more efficiently than possible by any classical means. The latter has sparked the now increasingly growing research field of quantum computation [6]. Owing to the unique features of quantum mechanics, such as superposition and entanglement, quantum computers have the potential to perform tasks utterly intractable on any conceivable classical computing hardware.

While different theoretical approaches of how to realize these quantum computers in the laboratory exist, one particular model excites the community because of its simplicity for experiments. It is an entanglement based scheme widely known as “one-way” quantum computing [7]. In this scheme the computation or information processing is performed by measuring particles that are part of a large entangled network. As with the coins, the state of all the particles in the network will be influenced according to the outcome of the measurement at a particular site. This allows to manipulate large arrays of quantum particles (usually called “cluster states”) and therefore to utilize their powerful features to execute algorithms in a speed and fashion impossible with a classical processor. Depending on which and how the individual particles are measured, the remaining particles will occupy different states [7]. Reading out this state will provide the user with the output of his computation. Because of the irreversibility of the measurement process (it collapses the quantum superposition to a definite state) the term “one-way” quantum computer was introduced.

In the experiments, we employ the polarization degree of freedom of single photons as our information carriers. A photon that carries horizontal polarization thus represents a qubit which is in the logical “0” state, while vertical polarization embodies “1”. However, we can also prepare photons whose polarization is along 45 degrees, thus representing “0+1”, i.e. it exists in a superposition of both basis states.

After entangling a certain number of these photons (qubits), we start to run our one-way quantum computer by measuring the photons polarizations in a certain order and fashion [8]. By doing so, the input information, represented by the initial state of some photons, is altered and processed due to the measurement task. Reading out the quantum state of the remaining photons yields the output of the computation. The larger the initial, entangled state, the more measurements can be performed and the more complex and powerful the computation.

In proof-of-principle experiments, small versions of these quantum computers have already been built [8,9]. In the most successful realization, a process called spontaneous parametric down-conversion is employed in order to create photon pairs (also known as Bell states) which are entangled in their polarization state. To generate large networks of entangled states, these entangled photon pairs are further subject to operations that combine the individual Bell states to yield large cluster states.

Using single photons as qubits has the advantage that their quantum state remains basically unaltered during the experiment, owing to the typically weak coupling of photons to their environment. Moreover, single photons can be conveniently controlled with standard optical components.

In the actual experiment, we utilized two Bell states to create a cluster state made up of four photons. Depending on the type and order of measurements on this cluster, different one-qubit and two-qubit operations could be realized, therefore demonstrating the working principles of such one-way quantum computers and the potential to perform even more complex computations. With this set of operations, the successful realization of a quantum algorithm has also been shown. Quantum algorithms [6] can execute certain tasks such as searching in an unsorted database with less elementary steps than classically possible. Take e.g. a database with N elements. A classical algorithm needs to look, on average, N/2 times into the database to find a desired entry. Grover’s quantum algorithm [10] masters this search tasks with only steps. In our experiment, the database consists of 4 entries, each embodied by a photon. Intriguingly, in this case, Grover’s algorithm finds the corresponding entry with unit fidelity after only a single run [8-10]. This has been verified in the experiment and our demonstrations will hopefully pave the way for the realization of even more complex quantum algorithms, such as Shor’s algorithm [11] for the efficient factorization of large integers into prime numbers – a method on which most of today’s encryption protocols rely.

**References:**

[1] Schrödinger, E. Die gegenwärtige Situation der Quantenmechanik. Die Naturwissenschaften 49, 823-828 (1935).

[2] Prevedel, R. et al. Photonic entanglement as a resource in quantum computation and quantum communication. J. Opt. Soc. Am. B 24, 241-248 (2007).

[3] Ekert, A. K. Quantum Cryptography Based on Bell's Theorem. Phys. Rev. Lett. 67, 661-663 (1991).

[4] Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and EPR channels. Phys. Rev. Lett. 70, 1895-1899 (1993).

[5] Bouwmeester, D. et al. Experimental Quantum Teleportation. Nature 390, 575 (1997).

[6] Deutsch, D. & Ekert, E. Quantum computation. Phys. World 11, 47-52 (1998).

[7] Raussendorf R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188-5191 (2001).

[8] Walther, P. et al. Experimental one-way quantum computing. Nature 434, 169-176 (2005).

[9] Prevedel, R. et al. High-speed linear optics quantum computing using active feed-forward. Nature 445, 65-69 (2007).

[10] Grover, L. K. Quantum mechanics helps in search for a needle in a haystack. Phys. Rev. Lett. 79, 325-328 (1997).

[11] Shor, P. W. Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science. Los Alamitos: IEEE Computer Society Press 124-134 (1994).

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