Arbitrary Pure State Research Articles

Proposal for direct measurement of concurrence via visibility in a cavity QED system

An experimental scheme is proposed that allows direct measurement of the concurrence of a two-qubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system.

Swap action in a solid-state controllable anisotropic Heisenberg model

Correct swap action can be realized via the control of the anisotropic Heisenberg interaction in solid-state quantum systems. The conditions of performing a swap are derived by the dynamics of arbitrary bipartite pure state. It is found that swap errors can be eliminated in the presence of symmetric anisotropy. In realistic quantum computers with unavoidable fluctuations, the gate fidelity of swap action is estimated. The scheme of quantum computation via the anisotropic Heisenberg interaction is implemented in a one-dimensional quantum dots. The slanting and static magnetic field can be used to adjust the anisotropy.

Probabilistic teleportation of an arbitrary pure state of two atoms

In the context of microwave cavity QED, this paper proposes a new scheme for teleportation of an arbitrary pure state of two atoms. The scheme is very different from the previous ones which achieve the integrated state measurement, it deals in a probabilistic but simplified way. In the scheme, no additional atoms are involved and thus only two atoms are required to be detected. The scheme can also be used for the teleportation of arbitrary pure states of many atoms or two-mode cavities.

Experimental remote preparation of arbitrary photon polarization states

We demonstrate an experiment for remote preparation of arbitrary photon polarization states. With local operations, polarization measurement, and one way classical communication, any states lying on and inside the Poincar\'e sphere can be remotely prepared. For arbitrary pure states, the efficiency is 100% with a communication cost of one entanglement bit and two classical bits. For mixed states, polarization insensitive measurement is introduced and the classical communication cost is one bit. Spontaneous parametric down-conversion (SPDC) is employed as an entanglement source. The remotely prepared qubits are estimated via quantum tomography process and fidelity between the experimentally prepared state and the expected state is considered to test the data. We achieve remote preparation of 13 states with fidelities all above 0.994.

Standard forms and entanglement engineering of multimode Gaussian states under local operations

We investigate the action of local unitary operations on multimode (pure or mixed) Gaussian states and single out the minimal number of locally invariant parameters which completely characterize the covariance matrix of such states. For pure Gaussian states, central resources for continuous-variable quantum information, we investigate separately the parameter reduction due to the additional constraint of global purity, and the one following by the local-unitary freedom. Counting arguments and insights from the phase-space Schmidt decomposition and in general from the framework of symplectic analysis, accompany our description of the standard form of pure n-mode Gaussian states. In particular, we clarify why only in pure states with n ⩽ 3 modes all the direct correlations between position and momentum operators can be set to zero by local unitary operations. For any n, the emerging minimal set of parameters contains complete information about all forms of entanglement in the corresponding states. An efficient state engineering scheme (able to encode direct correlations between position and momentum operators as well) is proposed to produce entangled multimode Gaussian resources, its number of optical elements matching the minimal number of locally invariant degrees of freedom of general pure n-mode Gaussian states. Finally, we demonstrate that so-called ‘block-diagonal’ Gaussian states, without direct correlations between position and momentum, are systematically less entangled, on average, than arbitrary pure Gaussian states.

Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox

The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.

Direct measurement of concurrence for atomic two-qubit pure states

We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one- and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing 3D microwave cavities and trapped ion systems.

Remote preparation of qutrit states with biphotons

We report an experimental demonstration of remote preparation of an arbitrary pure qutrit state. A qutrit is encoded in a two-photon (biphoton) polarization state. Prepared states are characterized by quantum state tomography. Experimental imperfection is discussed and evaluated by an experimentally obtained density matrix. The present scheme can develop into generation of an arbitrary two-photon triplet state and accordingly to an essential multiparty quantum communication protocol. Generalization to higher order which enables remote preparation of an arbitrary qudit state and several typical multiphoton entangled states is also shown.

Optical implementation of the encoding of two qubits to a single qutrit

We have devised an optical scheme for the recently proposed protocol for encoding two qubits into one qutrit. In this protocol, Alice encodes an arbitrary pure product state of two qubits into a state of one qutrit. Bob can then restore error-free any of the two encoded qubit states but not both of them simultaneously. We have successfully realized this scheme experimentally using spatial-mode encoding. Each qubit (qutrit) was represented by a single photon that could propagate through two (three) separate fibers. We theoretically propose two generalizations of the original protocol. We have found a probabilistic operation that enables to retrieve both qubits simultaneously with the average fidelity above 90% and we have proposed extension of the original encoding transformation to encode N qubits into one (N+1)-dimensional system.

Qubit feedback and control with kicked quantum nondemolition measurements: A quantum Bayesian analysis

The informational approach to continuous quantum measurement is derived from POVM formalism for a mesoscopic scattering detector measuring a charge qubit. Quantum Bayesian equations for the qubit density matrix are derived, and cast into the form of a stochastic conformal map. Measurement statistics are derived for kicked quantum nondemolition measurements, combined with conditional unitary operations. These results are applied to derive a feedback protocol to produce an arbitrary pure state after a weak measurement, as well as to investigate how an initially mixed state becomes purified with and without feedback.

Scheme for teleportation of atomic states within cavities in thermal states

An experimentally feasible scheme is proposed for the teleportation of an atomic state and of a two-atom entangled state within the microwave cavity quantum electrodynamics with unit probability of success. Our scheme is based on the interaction between atoms and a single-mode nonresonant cavity with the assistance of a strong classical driving field. Thus the teleportation scheme is insensitive to the thermal state. This idea can also be used to teleport an arbitrary two-atom pure state via two pairs of atomic Einstein-Podolsky-Rosen states in a straightforward way.

Stringy black holes and the geometry of entanglement

Recently striking multiple relations have been found between pure state two- and three-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theories. In particular, we show that finding the frozen values of the moduli in the calculation of the macroscopic black-hole entropy in the $STU$ model is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of finding the optimal local distillation protocol of a GHZ state from an arbitrary three-qubit pure state. These results and a geometric classification of $STU$ black holes, BPS and non-BPS can be described in the elegant language of twistors. Finally an interesting connection between the black-hole entropy and the average real entanglement of formation is established.

Optimal dense coding with arbitrary pure entangled states

We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense coding are derived. We also construct the optimal protocol which saturates the upper bound in each case.

No-partial erasure of quantum information

In complete erasure any arbitrary pure quantum state is transformed to a fixed pure state by irreversible operation. Here we ask if the process of partial erasure of quantum information is possible by general quantum operations, where partial erasure refers to reducing the dimension of the parameter space that specifies the quantum state. We prove that quantum information stored in qubits and qudits cannot be partially erased, even by irreversible operations. The ‘no-partial erasure’ theorem applies to spin and bosonic coherent states, and continuous variable quantum information schemes as well. Our theorem suggests an integrity principle that quantum information is indivisible.

Optimal conclusive teleportation of a d -dimensional two-particle unknown quantum state

A conclusive teleportation protocol of a d-dimensional two-particle unknown quantum state using three d-dimensional particles in an arbitrary pure state is proposed. A sender teleports the unknown state conclusively to a receiver by using the positive operator valued measure(POVM) and introducing an ancillary qudit to perform the generalized Bell basis measurement. We calculate the optimal teleportation fidelity. We also discuss and analyse the reason why the information on the teleported state is lost in the course of the protocol.

Dephasing representation of quantum fidelity for general pure and mixed states

A general semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none is due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for physical perturbations and for numerical errors. Beyond justifying the approximation, the shadowing theorem makes the dephasing representation practical: without shadowing it would be impossible to find numerically the precise trajectories needed in a semiclassical approximation. It is shown how the general expression reduces to the previously known special forms for localized states. The superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets, nonlocal pure states, and for simple and random mixed states. The tests are done in nonuniversal regimes in mixed phase space where detailed features of fidelity are important. Although semiclassically motivated, the present approach is valid for abstract systems with a finite Hilbert basis provided that the discrete Wigner transform is used. This makes the method applicable, via a phase-space approach, to problems of quantum computation.

Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence

We present a complete analysis of the multipartite entanglement of three-mode Gaussian states of continuous-variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations can be quantified by a proper convex roof extension of the squared logarithmic negativity, the continuous-variable tangle, or contangle. We review and elucidate in detail the proof that in multimode Gaussian states the contangle satisfies a monogamy inequality constraint [G. Adesso and F. Illuminati, New J. Phys8, 15 (2006)]. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communications and defines a measure of genuine tripartite entanglements. We determine the analytical expression of the residual contangle for arbitrary pure three-mode Gaussian states and study in detail the distribution of quantum correlations in such states. This analysis yields that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states $\mathrm{GHZ}∕W$ states of continuous-variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the $W$ states of three qubits. We finally consider the effect of decoherence on three-mode Gaussian states, studying the decay of the residual contangle. The $\mathrm{GHZ}∕W$ states are shown to be maximally robust against losses and thermal noise.

Efficient state preparation for a register of quantum bits

We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.

N-qubit entanglement via the [formula omitted]-type collective interaction

We investigate quantum correlations of the N-qubit states via a collective pseudo-spin interaction ( ∝ J y 2 ) on arbitrary pure separable states for a given interval of time. Based on this dynamical generation of the N-qubit maximal entangled states, a quantum secret sharing protocol with N continuous classical secrets is developed.

Information balance in quantum teleportation with an arbitrary pure state

We study a general teleportation scheme with an arbitrary two-party pure state and derive a tight bound of the teleportation fidelity with a predesigned estimation of the unknown state to be teleported. This bound shows a piecewise balance between information gain and state disturbance. We also explain possible physical significance of the balance.