Arbitrary Pure State Research Articles

Perfect Quantum Teleportation via Bell States

Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.

Quantum-Dot-Based Telecommunication-Wavelength Quantum Relay

The development of quantum relays for long haul and attack-proof quantum communication networks operating with weak coherent laser pulses requires entangled photon sources at telecommunication wavelengths with intrinsic single-photon emission for most practical implementations. Using a semiconductor quantum dot emitting entangled photon pairs in the telecom O-band, we demonstrate for the first time a quantum relay fulfilling both of these conditions. The system achieves a maximum fidelity of 94.5 % for implementation of a standard 4-state protocol with input states generated by a laser. We further investigate robustness against frequency detuning of the narrow-band input and perform process tomography of the teleporter, revealing operation for arbitrary pure input states, with an average gate fidelity of 83.6 %. The results highlight the potential of semiconductor light sources for compact and robust quantum relay technology, compatible with existing communication infrastructures.

Targeting pure quantum states by strong noncommutative dissipation

We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on the simultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limit of strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibrium steady state (NESS) of an open quantum system described by a Lindblad master equation approaches a target pure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formula for the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus paving the way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bell state, an arbitrary pure state of $N$ qubits, and a spin-helix state of $N$ qubits.

Quantification of concurrence via weak measurement

Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely concurrence, of an arbitrary two-qubit pure state via a single fixed measurement set-up by exploiting so-called weak measurements and the associated weak values together with the properties of the Laguerre-Gaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol.

A Total Measure of Multi-Particle Quantum Correlations in Atomic Schrödinger Cat States

We propose a total measure of multi-particle quantum correlation in a system of N two-level atoms (N qubits). We construct a parameter that encompasses all possible quantum correlations among N two-level atoms in arbitrary symmetric pure states and define its numerical value to be the total measure of the net atom-atom correlations. We use that parameter to quantify the total quantum correlations in atomic Schrödinger cat states, which are generated by the dispersive interaction in a cavity. We study the variation of the net amount of quantum correlation as we vary the number of atoms from N=2 to N=100 and obtain some interesting results. We also study the variation of the net correlation, for fixed interaction time, as we increase the number of atoms in the excited state of the initial system, and notice some interesting features. We also observe the behaviour of the net quantum correlation as we continuously increase the interaction time, for the general state of N two-level atoms in a dispersive cavity.

Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization

We study the entanglement entropy (EE) for pure gauge theories in 1[Formula: see text]+[Formula: see text]1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,1 we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1[Formula: see text]+[Formula: see text]1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.

Quantum state transfer control based on the optimal measurement

SummaryThis paper explores the optimal control of quantum state transfer in a two‐dimensional quantum system by a sequence of non‐selective projection measurements. We show that for a given initial state, one can always find the corresponding projection operator that can effectively drive the given initial state to any arbitrary target pure state. An external control field is proposed to compensate the effect of the free evolution of system. Numerical simulations and characteristics analysis are given in three cases: without considering free evolution, considering free evolution, and with the action of external control field. The simulating experimental results show that the optimal measurement control is more effective by using proposed external control field. Copyright © 2016 John Wiley & Sons, Ltd.

Quantum entanglement swapping of two arbitrary biqubit pure states

In this paper, the issue of swapping quantum entanglements in two arbitrary biqubit pure states via a local bipartite entangledstate projective measure in the middle node is studied in depth, especially with regard to quantitative aspects. Attention is mainly focused on the relation between the measure and the final entanglement obtained via swapping. During the study, the entanglement of formation (EoF) is employed as a quantifier to characterize and quantify the entanglements present in all involved states. All concerned EoFs are expressed analytically; thus, the relation between the final entanglement and the measuring state is established. Through concrete analyses, the measure demands for getting a certain amount of a final entanglement are revealed. It is found that a maximally entangled final state can be obtained from any two given initial entangled states via swapping with a certain probability; however, a peculiar measure should be performed. Moreover, some distinct properties are revealed and analyzed. Such a study will be useful in quantum information processes.

Entanglement-fluctuation relation for bipartite pure states

We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived fluctuation-entanglement relation is evaluated for the ground states of a one-dimensional free fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.

Entangling and assisted entangling power of bipartite unitary operations

Nonlocal unitary operations can create quantum entanglement between distributed particles, and the quantification of created entanglement is a hard problem. It corresponds to the concepts of entangling and assisted entangling power when the input states are, respectively, product and arbitrary pure states. We analytically derive them for Schmidt-rank-two bipartite unitary and some complex bipartite permutation unitaries. In particular, the entangling power of permutation unitary of Schmidt rank three can take only one of two values: $\log_2 9 - 16/9$ or $\log_2 3$ ebits. The entangling power, assisted entangling power and disentangling power of $2\times d_B$ permutation unitaries of Schmidt rank four are all $2$ ebits. These quantities are also derived for generalized Clifford operators. We further show that any bipartite permutation unitary of Schmidt rank greater than two has entangling power greater than $1.223$ ebits. We construct the generalized controlled-NOT (CNOT) gates whose assisted entangling power reaches the maximum. We quantitatively compare the entangling power and assisted entangling power for general bipartite unitaries, and study their connection to the disentangling power. We also propose a probabilistic protocol for implementing bipartite unitaries.

Stable pure state quantum tomography from five orthonormal bases

For any finite-dimensional Hilbert space, we construct explicitly five orthonormal bases such that the corresponding measurements allow for efficient tomography of an arbitrary pure quantum state. This means that such measurements can be used to distinguish an arbitrary pure state from any other state, pure or mixed, and the pure state can be reconstructed from the outcome distribution in a feasible way. The set of measurements we construct is independent of the unknown state, and therefore our results provide a fixed scheme for pure state tomography, as opposed to the adaptive (state-dependent) scheme proposed by Goyeneche et al. (Phys. Rev. Lett., 115 (2015) 090401). We show that our scheme is robust with respect to noise, in the sense that any measurement scheme which approximates these measurements well enough is equally suitable for pure state tomography. Finally, we present two convex programs which can be used to reconstruct the unknown pure state from the measurement outcome distributions.

Conditions for monogamy of quantum correlations in multipartite systems

Monogamy of quantum correlations is a vibrant area of research because of its potential applications in several areas in quantum information ranging from quantum cryptography to co-operative phenomena in many-body physics. In this paper, we investigate conditions under which monogamy is preserved for functions of quantum correlation measures. We prove that a monogamous measure remains monogamous on raising its power, and a non-monogamous measure remains non-monogamous on lowering its power. We also prove that monogamy of a convex quantum correlation measure for arbitrary multipartite pure quantum state leads to its monogamy for mixed states in the same Hilbert space. Monogamy of squared negativity for mixed states and that of entanglement of formation follow as corollaries of our results.

Loschmidt echo for quantum metrology

We propose a versatile Loschmidt echo protocol to detect and quantify multiparticle entanglement. It allows us to extract the quantum Fisher information for arbitrary pure states, and finds direct application in quantum metrology. In particular, the protocol applies to states that are generally difficult to characterize, as non-Gaussian states, and states that are not symmetric under particle exchange. We focus on atomic systems, including trapped ions, polar molecules, and Rydberg atoms, where entanglement is generated dynamically via long-range interaction, and show that the protocol is stable against experimental detection errors.

Elementary quantum gates in different bases

We introduce transformation matrix connecting sets of the displaced states with different displacement amplitudes. Arbitrary pure one-mode state can be represented in new basis of the displaced number (Fock) states ($$\alpha $$ź-representation) by multiplying the transposed transformation matrix on a column vector of initial state. Analytical expressions of the $$\alpha $$ź-representation of superposition of vacuum and single photon and two-mode squeezed vacuum are obtained. On the basis of the developed mathematical formalism, we consider the mechanism of interaction between qubits which is based on their displaced properties. Superposed coherent states deterministically displace target state on equal modulo but opposite on sign values. Registration of the single photon in auxiliary mode (probabilistic operation) results in constructive interference and gives birth to entangled hybrid state corresponding to outcome of elementary quantum gates. The method requires minimal number of resource and works in realistic scenario.

Separability Criterion for Arbitrary Multipartite Pure State Based on the Rank of Reduced Density Matrix

Nowadays, there are plenty of separability criteria which are used to detect entanglement. Many of them are limited to apply for some cases. In this paper, we propose a separability criterion for arbitrary multipartite pure state which is based on the rank of reduced density matrix. It is proved that the rank of reduced density matrices of a multipartite state is closely related to entanglement. In fact it can be used to characterize entanglement. Our separability criterion is a necessary and sufficient condition for detecting entanglement. Furthermore, it is able to help us find the completely separable form of a multipartite pure state according to some explicit examples. Finally it demonstrates that our method are more suitable for some specific case. Our separability criterion are simple to understand and it is operational.

Enhancing quantum Fisher information by utilizing uncollapsing measurements

Abstract As an indicator of estimation precision, quantum Fisher information (QFI) lies at the heart of quantum metrology theory. In this work, an effective scheme for enhancing QFI is proposed by utilizing quantum uncollapsing measurements. Two kinds of strategies for the arbitrary two-qubit pure state with weight parameter and phase parameter are implemented under different situations, respectively. We derive the explicit conditions for the optimal measurement strengths, and verify that the QFI can be improved quite well. Meanwhile, due to the relation of quantum correlation and QFI, the maximal value of QFI associated with phase parameter for pure state is always equal to 1. It is worth noting that the optimal measurement strength is only related to the weight parameter, as uncollapsing measurements operation does not induce any disturbance on the value of phase parameter. The scheme also can be extended to improve the parameter estimation precision for an N -qubit pure state. In addition, as an example, the situation of an arbitrary single-qubit state under amplitude damping channel is investigated. It is shown that our scheme also works well for enhancing QFI under decoherence.

High Fidelity Symmetric Telecloning and Entanglement Distribution of Spin Quantum States by Weak Measurement and Reversal

We propose a physical realization of robust symmetric telecloning scheme for spin quantum states by employing the weak measurement and reversal (WMR) operation. Using proper WMR, the ultrahigh telecloning fidelity and long distance of quantum state transfer with certain success probability can be achieved. More interestingly, the lowest average telecloning fidelity can attain 80 %, which is almost independent of the spin chain length. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the WMR operation indeed helps for protecting distributed entanglement.

Pure-state tomography with the expectation value of Pauli operators

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary $n$-qubit pure state among all quantum states. We show that only $11$ Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with $16$ measurements, and only $31$ Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with $64$ measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

Universal Continuous-Variable State Orthogonalizer and Qubit Generator.

We experimentally demonstrate a universal strategy for producing a quantum state that is orthogonal to an arbitrary, infinite-dimensional, pure input one, even if only a limited amount of information about the latter is available. Arbitrary coherent superpositions of the two mutually orthogonal states are then produced by a simple change in the experimental parameters. We use input coherent states of light to illustrate two variations of the method. However, we show that the scheme works equally well for arbitrary input fields and constitutes a universal procedure, which may thus prove a useful building block for quantum state engineering and quantum information processing with continuous-variable qubits.

Perfect quantum teleportation by four-particle cluster state

Two perfect quantum teleportation schemes for an unknown single-particle pure state and an arbitrary two-particle pure entangled state are proposed by using four-particle cluster state in this paper. As it is shown, the unknown single-particle pure state or the arbitrary two-particle pure entangled state can be teleported perfectly. The successful possibilities are both 100% and quantum channel fidelities are both 1 about these two schemes.