Fault-tolerant quantum computing requires gates which function correctly despite the presence of errors, and are scalable if the error probability-per-gate is below a threshold value. To date, no method has been described for calculating this probability from measurements on a gate. Here we introduce a technique enabling quantitative benchmarking of quantum-logic gates against fault-tolerance thresholds for any architecture. We demonstrate our technique experimentally using a photonic entangling-gate. The relationship between experimental errors and their quantum logic effect is non-trivial: revealing this relationship requires a comprehensive theoretical model of the quantum-logic gate. We show the first such model for any architecture, and find multi-photon emission--a small effect previously regarded as secondary to mode-mismatch--to be the dominant source of logic error. We show that reducing this will move photonic quantum computing to within striking distance of fault-tolerance.

In this letter, we show how a Josephson charge qubit coupled to a transmission line and a nanomechanical resonator may be used to implement Jahn-Teller models and Kerr nonlinearities. We show explicit implementations of simple Jahn-Teller Hamiltonians in our system, and propose the generation of the Yurke-Stoler state which is quantum superposition of a pair of distinguishable coherent states. This is achieved by effectively implementing Kerr nonlinearities induced by application of a strong external driving field.

We have computed the spectrum emitted spontaneously by an artificial atom coupled to an arbitrarily detuned single mode cavity, taking into account pure dephasing processes. We show that if the emitter is incoherent, the cavity can efficiently emit photons with its own spectral characteristics. This result sheds new light on puzzling recent experimental data obtained with quantum dots and semiconductor optical microcavities. Cavity spectral filtering induced by the emitter's decoherence can be exploited to produce photons with a high degree of indistinguishability.

In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density-matrix renormalization group (DMRG), which makes use of redundancies in the description of the state. Here we show that the achievable efficiency can be much better when performing DMRG in the Heisenberg picture (H-DMRG), as only the observable of interest but not the entire state is considered. In some non-trivial cases, H-DMRG can even be exact for finite bond dimensions.

It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities.

We find the allowed complex numbers associated with the inner product of N equally separated pure quantum states. The allowed areas on the unitary complex plane have the form of petals. A point inside the petal-shape represents a set of N linearly independent (LI) pure states, and a point on the edge of that area represents a set of N linearly dependent (LD) pure states. For each one of those LI sets we study the complete discrimination of its N equi-separated states combining sequentially the two known strategies: first the unambiguous identification protocol for LI states, followed, if necessary, by the error-minimizing measurement scheme for LD states. We find that the probabilities of success for both unambiguous and ambiguous discrimination procedures depend on both the module and the phase of the involved inner product complex number. We show that, with respect to the phase-parameter, the maximal probability of discriminating unambiguously the N non-orthogonal pure states holds just when there no longer be probability of obtaining ambiguously information about the prepared state by applying the second protocol if the first one was not successful.

We explicitate the relation between Hamiltonians for networks of interacting qubits in the XYZ model and graph Laplacians. We then study evolution in networks in which all sites can communicate with each other. These are modeled by the complete graph K_{n} and called all-to-all networks. It turns out that K_{n} does not exhibit perfect state transfer (PST). However, we prove that deleting an edge in K_{n} allows PST between the two non-adjacent sites, when n is a multiple of four. An application is routing a qubit over n different sites, by switching off the link between the sites that we wish to put in communication. Additionally, we observe that, in certain cases, the unitary inducing evolution in K_{n} is equivalent to the Grover operator.

We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method to provide two faithful copies of a two-photon mixed state required for parity measurements: Two photon pairs generated by two neighboring pump laser pulses through optical parametric down conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multi-photon mixed states.

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present a proof of this theorem which is both elementary and economical. Central to our proof is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis involves a judicious interplay between the effect a given Wigner symmetry has on certain two-dimensional subspaces and the effect it has on the entire Hilbert space.

The generalized n-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only pure states of n qubits that are not uniquely determined (among arbitrary states, pure or mixed) by their reduced density matrices of n-1 qubits. Thus, the generalized GHZ states are the only ones containing information at the n-party level.

The existence of a monotonic distance dependent contact potential between two plates in a Casimir experiment leads to an additional electrostatic force that is significantly different from the case of a constant potential. Such a varying potential can arise if there is a uniform gradient in the work function or contact potential across a plate, as opposed to random microscopic fluctuations associated with patch potentials. A procedure to compensate for this force is described for the case of an experiment where the electrostatic force is minimized at each measurement distance by applying a voltage between the plates. It is noted that the minimizing voltage is not the contact potential.

We consider ramifications of the use of high speed light modulators to questions of correlation and measurement of time-energy entangled photons. Using phase modulators, we find that temporal modulation of one photon of an entangled pair, as measured by correlation in the frequency domain, may be negated or enhanced by modulation of the second photon. Using amplitude modulators we describe a Fourier technique for measurement of biphoton wave functions with slow detectors.

We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.