Pair Of Quantum Bits Research Articles

Random Private Quantum States

The study of properties of randomly chosen quantum states has in recent years led to many insights into quantum entanglement. In this work, we study private quantum states from this point of view. Private quantum states are bipartite quantum states characterised by the property that carrying out simple local measurements yields a secret bit. This feature is shared by the maximally entangled pair of quantum bits, yet private quantum states are more general and can in their most extreme form be almost bound entangled. In this work, we study the entanglement properties of random private quantum states and show that they are hardly distinguishable from separable states and thus have low repeatable key, despite containing one bit of key. The technical tools we develop are centred around the concept of locally restricted measurements and include a new operator ordering, bounds on norms under tensoring with entangled states and a continuity bound for a relative entropy measure.

Entanglement distribution in optical fibers assisted by nonlocal memory effects

The successful implementation of several quantum information and communication protocols requires distributing entangled pairs of quantum bits in a reliable manner. While there exists a substantial amount of recent theoretical and experimental activities dealing with non-Markovian quantum dynamics, experimental application and verification of the usefulness of memory effects for quantum information tasks are still missing. We combine these two aspects and show experimentally that a recently introduced concept of nonlocal memory effects allows to protect and distribute polarization entangled pairs of photons in an efficient manner within polarization-maintaining (PM) optical fibers. The introduced scheme is based on correlating the environments, i.e. frequencies of the polarization entangled photons, before their physical distribution. When comparing to the case without nonlocal memory effects, we demonstrate at least a 12-fold improvement in the channel, or fiber length, for preserving the highly entangled initial polarization states of photons against dephasing.

Study of the cloning fidelities for the entanglement of a pair of quantum bits

The cloning fidelities is broadly investigated for the entanglement of a pair of quantum bits. Some new analytical descriptions of the cloning fidelities have been obtained for the entanglement of a pair of quantum bits, generalizing asymmetric cloning transformations and considering a special circumstance. We derive some intact mathematical expressions and simulation results, having the extensive physics meaning, for the investigation of the separability-preserving cloning machine that duplicates all entangled states of two qubits.

Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits

Quantum computation requires quantum logic gates that use the interaction within pairs of quantum bits (qubits) to perform conditional operations. Superconducting qubits may offer an attractive route towards scalable quantum computing. In previous experiments on coupled superconducting qubits, conditional gate behaviour and entanglement were demonstrated. Here we demonstrate selective execution of the complete set of four different controlled-NOT (CNOT) quantum logic gates, by applying microwave pulses of appropriate frequency to a single pair of coupled flux qubits. All two-qubit computational basis states and their superpositions are used as input, while two independent single-shot SQUID detectors measure the output state, including qubit-qubit correlations. We determined the gate's truth table by directly measuring the state transfer amplitudes and by acquiring the relevant quantum phase shift using a Ramsey-like interference experiment. The four conditional gates result from the symmetry of the qubits in the pair: either qubit can assume the role of control or target, and the gate action can be conditioned on either the 0-state or the 1-state. These gates are now sufficiently characterized to be used in quantum algorithms, and together form an efficient set of versatile building blocks.

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C^n tensor C^n whose operator-Schmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number S for every S in {1,...,9}. This corollary was unexpected, since it contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003) 052301] based on intuition from a striking result in the two-qubit case. By the results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901 quant-ph/0112124], who also considered the two-qubit case, our result implies that there are nine equivalence classes of unitaries on C^3 tensor C^3 which are probabilistically interconvertible by (stochastic) local operations and classical communication. As another corollary, a prescription is produced for constructing maximally-entangled operators from biunimodular functions. Reversing tact, we state a generalized operator-Schmidt decomposition of the quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 --> C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by Nielsen's bound) that the communication cost of the QFT remains maximal when a net transfer of qudits is permitted. In an appendix, a canonical procedure is given for removing basis-dependence for results and proofs depending on the "magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and quant-ph/9709029)].

Theory of a Pair of Quantum Bits

In this paper we present a thorough study of the theory of a pair of qubits, whose Hilbert space can be identified with ℂ2 ⊗ ℂ2. Given an hermitian operator ρ of trace 1 in ℂ2 ⊗ ℂ2 we focus on the following Problems: Problem 1: Find conditions that guarantee that ρ is a state, that is, positive semidefinite. Problem 2: Find conditions that guarantee that a given state ρ is separable, or that ρ is a convex combination of products of one-particle states. The language we develop for our investigation makes use of the observation that ℂ2 ⊗ ℂ2 carries representations of the special unitary group SU(2) in two dimensions and of the direct product of this group by itself. We introduce a new type of observable called Bell observable (section 5) and a new measure of entanglement called concurrence, which is closely related to the concurrence introduced by Wootters (Physical Review Letters (1998) 80, 2245–2248) (section 8). The work has been inspired by the works of Wootters (Physical Review Letters (1997) 78, 5022–5025; Physical Review Letters (1998) 80, 2245–2248) and members of the Horodecki family (cf Horodecki and Horodecki, Physical Review A (1996) 54, 1838–1843; Horodecki et al., Physics Letters A (1996a) 223, 1–8; Physics Letters A (1996b) 222, 21–25) and reproduces some of their results.

Exact Bures probabilities that two quantum bits are classically correlated

In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy to the (classical) Bayesian role of the volume elements ("Jeffreys' priors") of Fisher information metrics. Continuing this work, we obtain exact Bures probabilities that the members of certain low-dimensional subsets of the fifteen-dimensional convex set of 4 x 4 density matrices are separable or classically correlated. The main analytical tools employed are symbolic integration and a formula of Dittmann (quant-ph/9908044) for Bures metric tensors. This study complements an earlier one (quant-ph/9810026) in which numerical (randomization) --- but not integration --- methods were used to estimate Bures separability probabilities for unrestricted 4 x 4 or 6 x 6 density matrices. The exact values adduced here for pairs of quantum bits (qubits), typically, well exceed the estimate (.1) there, but this disparity may be attributable to our focus on special low-dimensional subsets. Quite remarkably, for the q = 1 and q = 1/2 states inferred using the principle of maximum nonadditive (Tsallis) entropy, the separability probabilities are both equal to 2^{1/2} - 1. For the Werner qubit-qutrit and qutrit-qutrit states, the probabilities are vanishingly small, while in the qubit-qubit case it is 1/4.

Efficient implementation of coupled logic gates for quantum computation

Most natural Hamiltonians do not couple specific pairs of quantum bits and spurious couplings occur along with the intended one. We present an efficient scheme that couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of n spins with pairwise coupling, the scheme concatenates $\mathrm{cn}$ intervals of system evolution and uses at most ${\mathrm{cn}}^{2}$ pulses where $c\ensuremath{\approx}1.$ Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.