arXiv subjects
Publications and source records attributed to M. B. Plenio.
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.
We present a task which can be faithfully solved with finite resources only when aided by particles prepared in a particular entangled state: the singlet state. The task consists of identifying the mutual parallelity or orthogonality of weak distant magnetic fields whose absolute directions are completely unknown.
We present an alternative scheme for the generation of a 2-qubit quantum gate interaction between laser-cooled trapped ions. The scheme is based on the AC Stark shift (lightshift) induced by laser light resonant with the ionic transition frequency. At {\it specific} laser intensities, the shift of the ionic levels allows the resonant excitation of transitions involving the exchange of motional quanta. We compare the performance of this scheme with respect to that of related ion-trap proposals and find that, for an experimental realisation using travelling-wave radiation and working in the Lamb-Dicke regime, an improvement of over an order of magnitude in the gate switching rate is possible.
We demonstrate that all good asymptotic entanglement measures are either identical or place a different ordering on the set of all quantum states.
Stochastic resonance shows that under some circumstances noise can enhance the response of a system to a periodic force. While this effect has been extensively investigated theoretically and demonstrated experimentally in classical systems, there is complete lack of experimental evidence within the purely quantum mechanical domain. Here we demonstrate that stochastic resonance can be exhibited in a single ion and would be experimentally observable using well mastered experimental techniques. We discuss the use of this scheme for the detection of the frequency difference of two lasers to demonstrate that stochastic resonance may have applications in precision measurements at the quantum limit.
We show how the state of an atom trapped in a cavity can be teleported to a second atom trapped in a distant cavity simply by detecting photon decays from the cavities. This is a rare example of a decay mechanism playing a constructive role in quantum information processing. The scheme is comparatively easy to implement, requiring only the ability to trap a single three level atom in a cavity.
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement and in terms of the average mutual distinguishability of the signal states.
We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using methods that have been developed for the optimal purification of mixed states we find a class of mixed states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.
We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.
We compare the entanglement of formation with a measure defined as the modulus of the negative eigenvalue of the partial transpose. In particular, we investigate whether both measures give the same ordering of density operators with respect to the amount of entanglement.
We investigate to what extent two trapped ions can be manipulated coherently when their coupling is mediated by a dipole-dipole interaction. We will show how the resulting level shift induced by this interaction can be used to create entanglement, while the decay of the states remains nearly negligible. This will allow us to implement conditional dynamics (a CNOT gate) and single qubit operations. We propose two different experimental realisations where a large level shift can be achieved and discuss both the strengths and weaknesses of this scheme from the point of view of a practical realization.
A quantum telecloning process combining quantum teleportation and optimal quantum cloning from one input to M outputs is presented. The scheme relies on the establishment of particular multiparticle entangled states, which function as multiuser quantum information channels. The entanglement structure of these states is analyzed and shown to be crucial for this type of information processing.
Purification schemes for multi-particle entangled states cannot be treated as straightforward extensions of those for two particles because of the lack of symmetry they possess. We propose purification protocols for a wide range of mixed entangled states of many particles. These are useful for understanding entanglement, and will be of practical significance in multi-user cryptographic schemes or distributed quantum computation and communication. We show that operating locally on multi-particle entangled states directly is more efficient than relying on two-particle purification.
Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations. In reality the quantum information processor (a linear ion trap, or cavity qed implementation for example) exists in a dissipative environment. Dephasing, and other technical sources of noise, as well as more fundamental sources of dissipation severely restrict quantum processing capabilities. The strength of the coherent coupling needed to implement quantum logic is not always independent of dissipation. The limitations these dissipative influences present will be described and the need for efficient error correction noted. Even if long and involved quantum computations turn out to be hard to realize, one can perform interesting manipulations of entanglement involving only a few gates and qubits, of which we give examples. Quantum communication also involves manipulations of entanglement which are simpler to implement than elaborate computations. We briefly analyse the notion of the capacity of a quantum communication channel.
We generalize previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the Quantum Relative Entropy and Bures Metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure which have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the Quantum Relative Entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure and that distillable entanglement is in general smaller than the entanglement of creation.
We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this notion to describe the amount of entanglement between two quantum systems from a statistical point of view. Our measure is independent of the number of entangled systems and their dimensionality.
The optimal precision of frequency measurements in the presence of decoherence is discussed. We analyze different preparations of n two level systems as well as different measurement procedures. We show that standard Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally entangled states provide the same resolution. The best resolution is achieved using partially entangled preparations with a high degree of symmetry.
We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.