Toward a more economical cluster state quantum computation

We assess the effects of an intrinsic model for imperfections in cluster states by introducing {\it noisy cluster states} and characterizing their role in the one-way model for quantum computation. The action of individual dephasing channels on cluster qubits is also studied. We show that the effect of non-idealities is limited by using small clusters, which requires compact schemes for computation. In light of this, we address an experimentally realizable four-qubit linear cluster which simulates a controlled-{\sf NOT} ({\sf CNOT}).Comment: 4 pages, 2 figures, RevTeX4; proposal for experimental setup include

High purity bright single photon source

Using cavity-enhanced non-degenerate parametric downconversion, we have built a frequency tunable source of heralded single photons with a narrow bandwidth of 8 MHz, making it compatible with atomic quantum memories. The photon state is 70% pure single photon as characterized by a tomographic measurement and reconstruction of the quantum state, revealing a clearly negative Wigner function. Furthermore, it has a spectral brightness of ~1,500 photons/s per MHz bandwidth, making it one of the brightest single photon sources available. We also investigate the correlation function of the down-converted fields using a combination of two very distinct detection methods; photon counting and homodyne measurement.Comment: 9 pages, 4 figures; minor changes, added referenc

Photon echo quantum memory with complete use of natural inhomogeneous broadening

The photon echo quantum memory is based on a controlled rephasing of the atomic coherence excited by signal light field in the inhomogeneously broadened resonant line. Here, we propose a novel active mechanism of the atomic rephasing which provides a perfect retrieval of the stored light field in the photon echo quantum memory for arbitrary initial inhomogeneous broadening of the resonant line. It is shown that the rephasing mechanism can exploit all resonant atoms which maximally increases an optical depth of the resonant transition that is one of the critical parameters for realization of highly efficient quantum memory. We also demonstrate that the rephasing mechanism can be used for various realizations of the photon echo quantum memory that opens a wide road for its practical realization.Comment: 6 pages, 4 figure

Monotonicity of quantum relative entropy revisited

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong sub-additivity of the von Neumann entropy, the Golden-Thompson trace inequality and the monotonicity of the Holevo quantity.The relation to quantum Markovian states is briefly indicated.Comment: 13 pages, LATEX fil

Kochen-Specker theorem as a precondition for secure quantum key distribution

We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each QKD protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.Comment: 4 pages, To appear in Phys. Rev.

Error Analysis For Encoding A Qubit In An Oscillator

In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev, and Preskill [quant-ph/0008040] described a method to encode a qubit in the continuous Hilbert space of an oscillator's position and momentum variables. This encoding provides a natural error correction scheme that can correct errors due to small shifts of the position or momentum wave functions (i.e., use of the displacement operator). We present bounds on the size of correctable shift errors when both qubit and ancilla states may contain errors. We then use these bounds to constrain the quality of input qubit and ancilla states.Comment: 5 pages, 8 figures, submitted to Physical Review

The Jamio{\l}kowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number kk and kk-positive maps

Positive maps which are not completely positive are used in quantum information theory as witnesses for convex sets of states, in particular as entanglement witnesses and more generally as witnesses for states having Schmidt number not greater than k. It is known that such witnesses are related to k-positive maps. In this article we propose a new proof for the correspondence between vectors having Schmidt number k and k-positive maps using Jamiolkowski's criterion for positivity of linear maps; to this aim, we also investigate the precise notion of the term "Jamiolkowski isomorphism". As consequences of our proof we get the Jamiolkowski criterion for complete positivity, and we find a special case of a result by Choi, namely that k-positivity implies complete positivity, if k is the dimension of the smaller one of the Hilbert spaces on which the operators act.Comment: 9 page

Distance measures to compare real and ideal quantum processes

With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate a set of criteria such a distance measure must satisfy to be both experimentally and theoretically meaningful. We then assess a wide range of possible measures against these criteria, before making a recommendation as to the best measures to use in characterizing quantum information processing.Comment: 15 pages; this version in line with published versio

Overcoming a limitation of deterministic dense coding with a non-maximally entangled initial state

Under two-party deterministic dense-coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state |Psi>. If |Psi> represents a maximally entangled state (i.e., each of its Schmidt coefficients is sqrt(1/d)), then Alice can convey to Bob one of d^2 distinct messages. If |Psi> is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice's qudit, it is impossible to encode d^2-1 messages. Encoding d^2-2 is possible; see, e.g., the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when |Psi> is not maximally entangled, the communications limit of d^2-2 messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of |Psi> is sufficiently close to sqrt(1/d). In this protocol, d^2-2 of the messages are encoded via unitary operations on Alice's qudit, and the final (d^2-1)-th message is encoded via a (non-trace-preserving) quantum operation.Comment: 18 pages, published versio

Teleportation of two-mode squeezed states

We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.Comment: Revtex, 5 pages, 3 eps figures, accepted for publication in Phys. Rev.