Cecilia C. López, Ariel Bendersky, Juan Pablo Paz, David G. Cory

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the $\chi$-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way.

## Tuesday, July 27, 2010

## Sunday, July 18, 2010

### Noise-Powered Probabilistic Concentration of Phase Information

Mario A. Usuga, Christian R. Mueller, Christoffer Wittmann, Petr Marek, Radim Filip, Christoph Marquardt, Gerd Leuchs, Ulrik L. Andersen

Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs [6 - 8]. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit utilizing a thermal noise source and a photon number subtraction scheme [9]. The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state prior to amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.

Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be circumvented by resorting to a probabilistic scheme as recently proposed and demonstrated in refs [6 - 8]. These amplifiers are based on highly non-classical resources in a complex interferometer. Here we demonstrate a probabilistic quantum amplifier beating the fundamental quantum limit utilizing a thermal noise source and a photon number subtraction scheme [9]. The experiment shows, surprisingly, that the addition of incoherent noise leads to a noiselessly amplified output state with a phase uncertainty below the uncertainty of the state prior to amplification. This amplifier might become a valuable quantum tool in future quantum metrological schemes and quantum communication protocols.

## Wednesday, July 7, 2010

### Adding control to arbitrary quantum operations

Xiao-Qi Zhou, Timothy C. Ralph, Pruet Kalasuwan, Mian Zhang, Alberto Peruzzo, Benjamin P. Lanyon, Jeremy L. O'Brien

Quantum computers promise exponential power for particular tasks, however, the complexity of quantum algorithms remains a major technological challenge. We have developed and demonstrated an architecture independent technique for adding control qubits to arbitrary quantum operations (unitary or otherwise) - a key requirement in many quantum algorithms. The technique is independent of how the operation is done and does not even require knowledge of what the operation is. In this way the technical problems of how to implement a quantum operation and how to add a control are separated. The number of computational resources required is independent of the depth of the operation and increases only linearly with the number of qubits on which it acts. Our approach will significantly reduce the complexity of quantum computations such as Shor's factoring algorithm and the near-term prospect of quantum simulations. We use this new approach to implement a number of two-qubit photonic quantum gates in which the operation of the control circuit is completed independent of the choice of quantum operation.

Quantum computers promise exponential power for particular tasks, however, the complexity of quantum algorithms remains a major technological challenge. We have developed and demonstrated an architecture independent technique for adding control qubits to arbitrary quantum operations (unitary or otherwise) - a key requirement in many quantum algorithms. The technique is independent of how the operation is done and does not even require knowledge of what the operation is. In this way the technical problems of how to implement a quantum operation and how to add a control are separated. The number of computational resources required is independent of the depth of the operation and increases only linearly with the number of qubits on which it acts. Our approach will significantly reduce the complexity of quantum computations such as Shor's factoring algorithm and the near-term prospect of quantum simulations. We use this new approach to implement a number of two-qubit photonic quantum gates in which the operation of the control circuit is completed independent of the choice of quantum operation.

### Probing general relativity using atom interferometry

T. van Zoest, N. Gaaloul, Y. Singh, H. Ahlers, W. Herr, S. T. Seidel, W. Ertmer, E. Rasel, M. Eckart, E. Kajari, S. Arnold, G. Nandi, W. P. Schleich, R. Walser, A. Vogel, K. Sengstock, K. Bongs, W. Lewoczko-Adamczyk, M. Schiemangk, T. Schuldt, A. Peters, T. Könemann, H. Müntinga, C. Lämmerzahl, H. Dittus, T. Steinmetz, T. W. Hänsch, J. Reichel

Albert Einstein’s insight that it is impossible to distinguish

Albert Einstein’s insight that it is impossible to distinguish

^{ }a local experiment in a "freely falling elevator" from one in^{ }free space led to the development of the theory of general relativity.^{ }The wave nature of matter manifests itself in a striking way^{ }in Bose-Einstein condensates, where millions of atoms lose their^{ }identity and can be described by a single macroscopic wave function.^{ }We combine these two topics and report the preparation and observation^{ }of a Bose-Einstein condensate during free fall in a 146-meter-tall^{ }evacuated drop tower. During the expansion over 1 second, the^{ }atoms form a giant coherent matter wave that is delocalized^{ }on a millimeter scale, which represents a promising source for^{ }matter-wave interferometry to test the universality of free^{ }fall with quantum matter.
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