Single-mode and two-mode nonclassical features of quasi-Werner state is explored and effect of photon addition on them is studied in a quantitative manner
The significance of photon addition in engineering the single- and two-mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, we analyzed the behavior of the Wigner function of two quasi-Werner states theoretically constructed by superposing two normalized bipartite $m$-photon added coherent states. This allowed us to quantify the amount of nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured in terms of concurrence, entanglement of formation, and quantum discord. The WLN for a two-mode state corresponds to the sum of the single-mode nonclassicality as well as quantum correlations, and both of these are observed to enhance with photon addition manifesting the efficacy of photon addition in the entanglement distillation. Usefulness of photon addition is further established by showing that the performance of the quasi-Werner states as quantum channel for the teleportation of a single-mode coherent and squeezed states, as quantified via teleportation fidelity, improves with the photon addition. Further, in contrast to a set of existing results, it is established that the negative values of two-mode Wigner function cannot be used in general as a witness of quantum correlation.
We investigate the separability, nonlocality and squeezing of continuous-variable analogue of the Werner state: a mixture of pure two-mode squeezed vacuum state with local thermal radiations. Utilizing this Werner state, coherent-state teleportation in Braunstein-Kimble setup is discussed.
Transfer of entanglement and information is studied for quantum teleportation of an unknown entangled state through noisy quantum channels. We find that the quantum entanglement of the unknown state can be lost during the teleportation even when the channel is quantum correlated. We introduce a fundamental parameter of correlation information which dissipates linearly during the teleportation through the noisy channel. Analyzing the transfer of correlation information, we show that the purity of the initial state is important in determining the entanglement of the replica state.
In this paper we extend our recent results for quantum teleportation of single qubit pure information state using non-maximally entangled pure state resource [Quantum Inf Process, 11 (2012) 1251] to the case of a general mixed information state and mixed Werner states resource. Fidelity is found dependent on information state in general. We minimize it over all possible information states and maximize it over possible unitary transformations which can be done by the receiver to obtain a value dependent on purity of information state and mixing parameter of Werner states. For pure information s…
We study the efficacy of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separa…
Adopting an approach similar to that of Zukowski [Phys. Rev. A 62, 032101 (2000)], we investigate connections between teleportation and nonlocality. We derive a Bell-type inequality pertaining to the teleportation scenario and show that it is violated in the case of teleportation using a perfect singlet. We also investigate teleportation using `Werner states' of the form x P + (1-x) I/4, where P is the projector corresponding to a singlet state and I is the identity. We find that our inequality is violated, implying nonlocality, if x > 1/sqrt(2). In addition, we extend Werner's local hidden va…
Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial construction builds a unitary error basis from a family of Hadamard matrices and a Latin square. In this dissertation, I give a new categorical axiomatisation of Latin squares, and use this to give a fully graphical presentation and proof of the correctness of Werner's construction. The categorical approach makes clear that some of the Latin square axioms are unnecessa…
The class of quantum states known as Werner states have several interesting properties, which often serve to illuminate unusual properties of quantum information. Closely related to these states are the Holevo-Werner channels whose Choi matrices are Werner states. Exploiting the fact that these channels are teleportation covariant, and therefore simulable by teleportation, we compute the ultimate precision in the adaptive estimation of their channel-defining parameter. Similarly, we bound the minimum error probability affecting the adaptive discrimination of any two of these channels. In this …
Entanglement and mixedness of a bipartite mixed state resource are crucial for the success of quantum teleportation. Upper bounds on measures of mixedness, namely, von Neumann entropy and linear entropy beyond which the bipartite state ceases to be useful for quantum teleportation are known in the literature. In this work, we generalize these bounds and obtain rank dependent upper bounds on von Nuemann entropy and linear entropy for an arbitrary bipartite mixed state resource. We observe that the upper bounds on measures of mixedness increase with increase in the rank. For two qubit mixed stat…
We introduce a Werner-like mixture [R. F. Werner, Phys. Rev. A {\bf 40}, 4277 (1989)] by considering two correlated but different degrees of freedom, one with discrete variables and the other with continuous variables. We evaluate the mixedness of this state, and its degree of entanglement establishing its usefulness for quantum information processing like quantum teleportation. Then, we provide its tomographic characterization. Finally, we show how such a mixture can be generated and measured in a trapped system like one electron in a Penning trap.
We demonstrate Werner-like polarization-entangled state generation disapproving local hidden variable theory from a single semiconductor quantum dot. By exploiting tomographic analysis with temporal gating, we find biphoton states are mapped on the Werner state, which is crucial for quantum information applications due to its versatile ramifications such as usefulness to teleportation. Observed time evolution of the biphoton state brings us systematic understanding on a relationship between tomographically reconstructed biphoton state and a set of parameters characterizing exciton state includ…
Partial teleportation of entanglement is to teleport one particle of an entangled pair through a quantum channel. This is conceptually equivalent to quantum swapping. We consider the partial teleportation of entanglement in the noisy environment, employing the Werner-state representation of the noisy channel for the simplicity of calculation. To have the insight of the many-body teleportation, we introduce the measure of correlation information and study the transfer of the correlation information and entanglement. We find that the fidelity gets smaller as the initial-state is entangled more f…
Werner states have a host of interesting properties, which often serve to illuminate the unusual properties of quantum information. Starting from these states, one may define a family of quantum channels, known as the Holevo-Werner channels, which themselves afford several unusual properties. In this paper we use the teleportation covariance of these channels to upper bound their two-way assisted quantum and secret-key capacities. This bound may be expressed in terms of relative entropy distances, such as the relative entropy of entanglement, and also in terms of the squashed entanglement. Mos…
We analyze the performance of quantum teleportation in terms of average fidelity and fidelity deviation. The average fidelity is defined as the average value of the fidelities over all possible input states and the fidelity deviation is their standard deviation, which is referred to as a concept of fluctuation or universality. In the analysis, we find the condition to optimize both measures under a noisy quantum channel---we here consider the so-called Werner channel. To characterize our results, we introduce a two-dimensional space defined by the aforementioned measures, in which the performa…
Recently, the authors [arXiv quant-ph 1209.3706] studied quantum discord for Werner mixed states based on the four entangled coherent states, which are used for quantum teleportation of single qubit information encoded in superposed coherent state and compared it with entanglement of formation. In the present paper, we consider two more general bipartite superposed coherent states and get two quasi-Werner states. We study quantum discord and entanglement of formation for these states and compare them.
Present work is an attempt to compare quantum discord and quantum entanglement of Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, two based on maximally ECS are exactly similar to the perfect Werner state, while the rest two, based on non-maximally ECS, which are called quasi-Werner states behave in somewhat different ways and their quantum discord and entanglement depends on the coherent amplitude and the measurement basis.
In order to understand the resourcefulness of a natural quantum system in quantum communication tasks, we study the dense coding capacity (DCC) and teleportation fidelity (TF) of Haar uniformly generated random multipartite states of various ranks. We prove that when a rank-2 two-qubit state, a Werner state, and a pure state possess the same amount of entanglement, the DCC of a rank-2 state belongs to the envelope made by pure and Werner states. In a similar way, we obtain an upper bound via the generalized Greenberger-Horne-Zeilinger state for rank-2 three-qubit states when the dense coding w…
Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of non-classical correlation of an arbitrary quantum system in terms of its minimal distance from the set of classical states, in terms of teleportation fidelity for general two qubit and $d \otimes d$ dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two qubit state must violate the Bell inequality. This is illustrated by…
We begin this thesis by expanding the technique of teleportation simulation, which adds noise to the entangled resource state to mimic channel effects. By introducing classical noise in the communication step, we show it is possible to simulate more than just Pauli channels using teleportation. This new class is characterised, and studied in detail for a particular resource state, leading to a family of simulable channels named "Pauli-Damping channels" whose properties are analysed. Also introduced are a new family of quantum states, "phase Werner" states, whose entanglement properties relate …
Ideal quantum teleportation transfers an unknown quantum state intact from one party Alice to the other Bob via the use of a maximally entangled state and the communication of classical information. If Alice and Bob do not share entanglement, the maximal average fidelity between the state to be teleported and the state received, according to a classical measure-and-prepare scheme, is upper bounded by a function $f_{\mathrm{c}}$ that is inversely proportional to the Hilbert space dimension. In fact, even if they share entanglement, the so-called teleportation fidelity may still be less than the…
Quantum teleportation is a fundamental concept in quantum physics which now finds important applications at the heart of quantum technology including quantum relays, quantum repeaters and linear optics quantum computing (LOQC). Photonic implementations have largely focussed on achieving long distance teleportation due to its suitability for decoherence-free communication. Teleportation also plays a vital role in the scalability of photonic quantum computing, for which large linear optical networks will likely require an integrated architecture. Here we report the first demonstration of quantum…
Quantum Defect Analysis and Target-Orbit-Directed Correction via the Purpose-Oriented Framework: Applications to Entanglement Repairability and Teleportation Activation
Harbin Engineering University（哈尔滨工程大学）；Central South University（中南大学）；Zhejiang University（浙江大学）
In this paper we provide a novel way to explore the relation between quantum teleportation and quantum phase transition. We construct a quantum channel with a mixed state which is made from one dimensional quantum Ising chain with infinite length, and then consider the teleportation with the use of entangled Werner states as input qubits. The fidelity as a figure of merit to measure how well the quantum state is transferred is studied numerically. Remarkably we find the first-order derivative of the fidelity with respect to the parameter in quantum Ising chain exhibits a logarithmic divergence…
Tight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
Central High School（中央高中）；Department of Mathematics, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校数学系）；Department of Physics, University of Rhode Island（罗德岛大学物理系）
We obtain the maximal average fidelity corresponding to the standard quantum teleportation protocol for an arbitrary isotropic distribution of input states and an arbitrary resource state. We extend this result to a family of von Neumann measurements, which includes the projections onto the computational and Bell basis, considering a Bell-diagonal resource state. We focus on three specific isotropic distributions of input states: 1) completely mixed input states, 2) states with a certain (fixed) degree of purity, and 3) quasi-pure input states. We show that the standard quantum teleportation p…
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubi…
The academic research into entanglement nicely illustrates the interplay between fundamental science and applications, and the need to foster both aspects to advance either one. For instance, the possibility to distribute entangled photons over tens or even hundreds of kilometers is fascinating because it confirms the quantum predictions over large distances, while quantum theory is often presented to apply to the very small (see Figure 1). On the other hand, entanglement enables quantum key distribution (QKD) [1]. This most advanced application of quantum information processing allows one to …
Generative Adversarial Networks for Resource State Generation
Centre for Quantum Science and Technology, International Institute of Information Technology, Hyderabad（量子科学与技术中心，国际信息技术研究所，海得拉尔）；Center for Security Theory and Algorithmic Research, International Institute of Information Technology, Hyderabad（安全理论与算法研究中心，国际信息技术研究所，海得拉尔）；TCS Research, TATA Consultancy Services, India（TCS研究，塔塔咨询公司，印度）
We study the dynamics of entanglement of two electron spins in two quantum dots, in which each electron is interacting with its nuclear spin environment. Focusing on the case of uncoupled dots, and starting from either Bell or Werner states of two qubits, we calculate the decay of entanglement due to the hyperfine interaction with the nuclei. We mostly focus on the regime of magnetic fields in which the bath-induced electron spin flips play a role, for example their presence leads to the appearance of entanglement sudden death at finite time for two qubits initialized in a Bell state. For thes…
We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (u…
