Quantum Physics

Quantum coin tossing is a cryptographic task in which two parties, Alice and Bob, wish to generate a shared random bit but do not necessarily trust each other. This task is completely impossible to realize with classical asynchronous communication but becomes at least partially feasible when quantum communication is also available. The best quantum protocol known so far, due to Ambainis, uses qutrits and is near optimal in the sense that either party can bias the outcome with at most a 75% probability of success. However, when the transmission of the link is below 50%, Ambainis'  protocol can be easily broken by a cheating Bob. This problem arises whenever there exists a conclusive measurement allowing Bob to obtain with certainty, although with a probability less than one, relevant information about the state sent by Alice. In this talk, we will present a new protocol for quantum coin tossing that does not suffer from this weakness and, as a consequence, is loss-tolerant. We discuss possible attacks and argue that the protocol is secure. Technologically, the implementation of this protocol is no more difficult than implementing entangled quantum key distribution with qubits. This is joint work with Guido Berlin, Gilles Brassard and Nicolas Godbout.

The notion of weak-degradability of quantum channels is introduced by generalizing the degradability definition given by Devetak and Shor.  Exploiting the unitary equivalence with beam-splitter/amplifier channels we then prove that a large class of one-mode Bosonic Gaussian channels are either weakly degradable or anti-degradable. In the latter case this implies that their quantum capacity Q is null. In the former case instead, this allows us to establish the additivity of the coherent information  for those maps which admit unitary representation with single-mode pure environment.

The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most general method for encoding quantum information is to encode it into a subsystem, there exists a novel form of quantum error correction beyond the traditional quantum error correcting subspace codes. These new quantum error correcting subsystem codes differ from subspace codes in that their quantum correcting routines can be considerably simpler than related subspace codes. Here we present a class of quantum error correcting subsystem codes constructed from two classical linear codes. These codes are the subsystem versions of the quantum error correcting subspace codes which are generalizations of Shor’s original quantum error correcting subspace codes. For every Shor-type code, the codes we present give a considerable savings in the number of stabilizer measurements needed in their error recovery routines.

In quantum information, one can prove that a secure quantum cryptography channel based on photon key distribution requires reliable single photon sources. If not, a potential eavesdropper may be able to get information using the extra photons. Current sources are based on either attenuated laser beams, which may produce randomly 2 or even more photons at a time following a poissonian statistics, or either based on two level-systems providing single photon sources often requiring cooling or complex set-ups.The goal of our experiment is to provide an easy, robust and compact single photon source using nonlinear optics (parametric down-conversion). We want to study its statistics and compare it to other photon sources. We could use this heralded single photon source to create a quantum communication channel.

In nearly every quantum algorithm which exponentially outperforms the best classical algorithm the quantum Fourier transform plays a central role. Recently, however, cracks in the quantum Fourier transform paradigm have begun to emerge. In this talk I will discuss one such development which arises in a new efficient quantum algorithm for the Heisenberg hidden subgroup problem. In particular I will show how considerations of symmetry for this hidden subgroup problem lead naturally to a different transform than the quantum Fourier transform, the Clebsch-Gordan transform over the Heisenberg group. Clebsch-Gordan transforms over finite groups thus appear to be an important new tool for those attempting to find new quantum algorithms. [Part of this work was done in collaboration with Andrew Childs (Caltech) and Wim van Dam (UCSB)]

I will survey recent feasibility results on building multi-party cryptographic protocols which manipulate quantum data or are secure against quantum adversaries. The focus will be protocols for secure evaluation of quantum circuits. Along the way, I'll discuss how quantum machines can (and can't) prove knowledge of a secret to a distrustful partner. The talk is based on recent unpublished results, as well as older joint work with subsets of Michael Ben-Or, Claude Crepeau, Daniel Gottesman, and Avinatan Hasidim (STOC '02, FOCS '02, Eurocrypt '05, FOCS '06).

Inelastic collisions occur in Bose-Einstein condensates, in some cases, producing particle loss in the system. Nevertheless, these processes have not been studied in the case when particles do not escape the trap. We show that such inelastic processes are relevant in quantum properties of the system such as the evolution of the relative population and entanglement. Moreover, including inelastic terms in the models of multimode condensates allows for an exact analytical solution. 

After a brief overview of the three broad classes of superconducting quantum bits (qubits)--flux, charge and phase--I describe experiments on single and coupled flux qubits. The quantum state of a flux qubit is measured with a Superconducting QUantum Interference Device (SQUID). Single flux qubits exhibit the properties of a spin-1/2 system, including superposition of quantum states, Rabi oscillations and spin echoes. Two qubits, coupled by their mutual inductance and by screening currents in the readout SQUID, produce a ground state |0> and three excited states |1>, |2> and |3>. Microwave spectra reveal an anticrossing between the |1>and |2> energy levels. The level repulsion can be reduced to zero by means of a current pulse in the SQUID that changes its dynamic inductance and hence the coupling between the qubits. The results are in good agreement with predictions. The ability to switch the coupling between qubits on and off permits efficient realization of universal quantum logic. This work was in collaboration with T. Hime, B.L.T. Plourde, P.A. Reichardt, T.L. Robertson, A. Ustinov, K.B. Whaley, F.K. Wilhelm and C.-E. Wu, and supported by AFOSR, ARO and NSF.

Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is excluded.) In this talk I show how states that minimize uncertainty in this sense can be generated via a discrete phase space based on finite fields. I also discuss some numerically observed features of these minimum-uncertainty states as the dimension d gets very large.

We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.