Given an ensemble of n spins, at least some of which are partially polarized, we investigate the sharing of this polarization within a subspace of k spins. We assume that the sharing results in a pseudopure state, characterized by a single purity parameter which we call the bias. As a concrete example we consider ensembles of spin-1/2 nuclei in liquid-state nuclear magnetic resonance (NMR) systems. The shared bias levels are compared with some current entanglement bounds to determine whether the reduced subspaces can give rise to entangled states.
We present an economical setup for faithful entanglement sharing against collective noise. It is composed of polarizing beam splitters, half wave plates, polarization independent wavelength division multiplexers, and frequency shifters. An arbitrary qubit error on the polarization state of each photon in a multi-photon system caused by the noisy channel can be rejected, without resorting to additional qubits, fast polarization modulators, and nondestructive quantum nondemolition detectors. Its success probability is in principle 100%, which is independent of the noise parameters, and it can be…
We describe and experimentally demonstrate a three-party quantum secret sharing protocol using polarization-entangled photon pairs. The source itself serves as an active participant and can switch between the required photon states by modulating the pump beam only, thereby making the protocol less susceptible to loss and amenable to fast switching. Compared to three-photon protocols, the practical efficiency is dramatically improved as there is no need to generate, transmit, or detect a third photon.
One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many body systems which cannot be accessed locally. We show however that, remarkably, two-dimensional subspaces do not have this property: any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multi-partite structure, may be pe…
In single-qubit quantum secret sharing, a secret is shared between N parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all N parties in sequence; the secret is encoded in the first participant's preparation of the qubit state and the subsequent participants' choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol's security against eavesdropping attack under common experim…
Based on spin-orbit coupling induced by q-plates, we present a feasible experimental proposal for preparing two-dimensional spatially inhomogeneous polarizations of light. We further investigate the quantum correlations between these inhomogeneous polarizations of photon pairs generated by spontaneous parametric down-conversion, which in essence describe the so-called hypoentanglement that is established between composite spin-orbit variables of photons. The violation of the Clauser-Horne-Shimony-Holt-Bell inequality is predicted with S=2\sqrt2 to illustrate the entangled nature of the cylindr…
We propose a new quantum secret sharing scheme using a single non-entangled qubit. In the scheme, by transmitting a qubit to the next party sequentially, a sender can securely transmit a secret message to $N$ receivers who could only decode the message cooperatively after randomly shuffling the polarization of the qubit. We explain this quantum secret sharing scheme into the one between a sender and two receivers, and generalize the scheme between a sender and $N$ receivers. Since our scheme is capable of using a faint coherent pulse as a qubit, it is experimentally feasible within current tec…
We propose easy implementable protocols for robust quantum key distribution with the collective dephasing channel or collective rotating channel. In these protocols, Bob only takes passive photon detection to measure the polarization qubits in the random bases. The source for the protocol with collective rotating channel is made by type 2 spontaneous parametric down conversion with random unitary rotation and phase shifter, no quantum disentangler is required. A simple proof for unconditionally security is shown.
Quantum secret sharing (QSS) is a protocol to split a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. In the scheme, three parties Alice, Bob and Charlie first share a three-photon entangled state, Charlie can then force Alice and Bob to cooperate to be able to establish the secret key with him by performing proper polarization measurements on his photon and announcing which polarization basis he has chosen. In a similar manner, in third-man quantum cryptography (TQC) the third-man, Charlie, can control whether Alice and Bob can c…
The orbital angular momentum of photons, being defined in an infinitely dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed op…
Quantum key distribution with decoherence-free subspaces has been proposed to overcome the collective noise to the polarization modes of photons flying in quantum channel. Prototype of this scheme have also been achieved with parametric-down conversion source. However, a novel type of photon-number-splitting attack we proposed in this paper will make the practical implementations of this scheme insecure since the parametric-down conversion source may emit multi-photon pairs occasionally. We propose decoy states method to make these implementations immune to this attack. And with this decoy sta…
we experimentally implement a fault-tolerant quantum key distribution protocol with two photons in a decoherence-free subspace (DFS). It is demonstrated that our protocol can yield good key rate even with large bit-flip error rate caused by collective rotation, while the usual realization of BB84 protocol cannot produce any secure final key given the same channel. Since the experiment is performed in polarization space and does not need the calibration of reference frame, important applications in free-space quantum communication are expected. Moreover, our method can also be used to robustly …
Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model
Dokuz Eylul University（德格埃尤尔大学）；Izmir Institute of Technology（伊兹密尔理工学院）
We experimentally demonstrate a proposal [Phys. Rev. A 87, 052325 (2013)] of a scheme for robust distribution of polarization entangled photon pairs over collective noisy channels having the reciprocity. Although the scheme employs the robustness of two qubit decoherence-free subspace, by utilizing the forward propagation of one half of the entangled photons and the backward propagation of a classical reference light, it achieves an entanglement-sharing rate proportional to the transmittance of the quantum channel for the signal photon. We experimentally observed the efficient sharing rate whi…
We study distribution schemes for a polarization entangled photon pair based on a decoherence-free subspace over lossy quantum channels and propose an efficient scheme that is robust against not only collective phase noises but also general collective noises for two qubits. While the proposed scheme employs two photons to build the decoherence-free subspace, the success probability is proportional to the channel transmittance of a single photon with the aid of a counter-propagating weak coherent light pulse. The key ingredient in the scheme is found to be the reciprocity of the channel. The pr…
We present two polarization-based protocols for quantum key distribution. The protocols encode key bits in noiseless subspaces or subsystems, and so can function over a quantum channel subjected to an arbitrary degree of collective noise, as occurs, for instance, due to rotation of polarizations in an optical fiber. These protocols can be implemented using only entangled photon-pair sources, single-photon rotations, and single-photon detectors. Thus, our proposals offer practical and realistic alternatives to existing schemes for quantum key distribution over optical fibers without resorting t…
We make an explicit connection between fundamental notions in quantum cryptography and quantum error correction. Error-correcting subsystems (and subspaces) for quantum channels are the key vehicles for contending with noise in physical implementations of quantum information-processing. Private subsystems (and subspaces) for quantum channels play a central role in cryptographic schemes such as quantum secret sharing and private quantum communication. We show that a subsystem is private for a channel precisely when it is correctable for a complementary channel. This result is shown to hold even…
We introduce a method to distribute memory effects among different subspaces of an open two-qubit system's state space. Within the linear optical framework, our system of interest is the polarization of two photons, while the environment consists of their frequency degree of freedom. By exploiting initially correlated frequency distributions and initial frequency-dependent phase factors, we are able to control all the four decoherence functions for polarization -- corresponding to different open system subspace divisions -- almost independently of each other. Hence, our results demonstrate how…
Stable sources of entangled photons are important requirements for quantum communications. In recent years, cascaded downconversion has been demonstrated as an effective method of directly producing three-photon entanglement. However, to produce polarization entanglement these sources have until now relied on intricate active phase stabilization schemes, thus limiting their robustness and usability. In this work, we present a completely phase-stable source of three-photon entanglement in the polarization degree of freedom. With this source, which is based on a cascade of two pair sources based…
We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier transform, and show that these observables, when restricted to the one photon per mode subspace, reproduce the canonical position-momentum commutation relations. As a consequence, frequency and time operators can be used to define a universal set of gates in this particular subspace. We discuss the physical implementation of these gates as well as their effect…
We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherence free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one photon loss, and can be demonstrated with photon quadruplets using currently available technology.
Experimental Efficient Source-Independent Quantum Secret Sharing against Coherent Attacks
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院，先进微结构协同创新中心）；School of Physics and Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学物理学院，量子态构建与操控教育部重点实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine learning platform based on a Quantum Variational Autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar st…
We investigate coherence in one- and two-photon optical systems, both theoretically and experimentally. In the first case, we develop the density operator representing a single photon state subjected to a non-dissipative coupling between observed (polarization) and unobserved (frequency) degrees of freedom. We show that an implementation of ``bang-bang'' quantum control protects photon polarization information from certain types of decoherence. In the second case, we investigate the existence of a "decoherence-free" subspace of the Hilbert space of two-photon polarization states under the acti…
We observe polarization-entanglement between four photons produced from a single down-conversion source. The non-classical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well-suited for implementing advanced quantum communication schemes such as multi-party quantum key distribution, secret sharing and telecloning.
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any external potential present. The system is classical, set in a six-dimensional space and involves vacuum polarization as the background process. Basic vacuum polarization energy characterised oscillators are identified and then in assemblies are analysed in terms of energy occurrence frequencies. The orbits of polarization monopoles are given and shown to be …
We experimentally generate and characterize a six-photon polarization entangled state, which is usually called "Psi 6 +". This is realized with a filtering procedure of triple emissions of entangled photon pairs from a single source, which does not use any interferometric overlaps. The setup is very stable and we observe the six-photon state with high fidelity. The observed state can be used for demonstrations of telecloning and secret sharing protocols.
We present the experimental results of measurements of the overlap of both pure and mixed polarization states of photons. The fidelity and purity of mixed states were also measured. The experimental apparatus exploits the fact that a beam splitter can distinguish the singlet Bell state from the other Bell states, i.e., it realizes projections into the symmetric and antisymmetric subspaces of photons' Hilbert space.
The super-sensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots -- phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point of the sensor to a less vulnerable phase value. We present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of…
We investigate the time-evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion-core. Since the standard procedure is numerically prohibitive in this case, we propose a novel way to quantify the quantum correlation in such a system: we use the reduced density matrices of the directional subspaces along the polarization of the laser pulse and along the transverse directions as building blocks for an approximate entanglement entropy. We present our results, based on accurate numerical simulations, in terms of several of these entropi…
We present a state transfer protocol that is mathematically equivalent to quantum teleportation, but uses classical nonseparability instead of quantum entanglement. In our implementation we take advantage of nonseparability among three parties: orbital angular momentum (OAM), polarization, and the radial degrees of freedom of a beam of light. We demonstrate the transfer of arbitrary OAM states, in the subspace spanned by any two OAM states, to the polarization of the same beam.
Using polarization-entangled photons from spontaneous parametric downconversion, we have implemented Ekert's quantum cryptography protocol. The near-perfect correlations of the photons allow the sharing of a secret key between two parties. The presence of an eavesdropper is continually checked by measuring Bell's inequalities. We investigated several possible eavesdropper strategies, including pseudo-quantum non-demolition measurements. In all cases, the eavesdropper's presence was readily apparent. We discuss a procedure to increase her detectability.
True decoherence-free-subspace derived from a semiconductor double quantum dot Heisenberg spin-trimer
Seoul National University（首尔大学）；École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Weizmann Institute of Science（魏茨曼科学研究所）；Korea Research Institute of Standards and Science（韩国标准科学研究院）；Pusan National University（釜山国立大学）
An electron confined in a quantum dot interacts with its local nuclear spin environment through the hyperfine contact interaction. This interaction combined with external control and relaxation or measurement of the electron spin allows for the generation of dynamic nuclear polarization. The quantum nature of the nuclear bath, along with the interplay of coherent external fields and incoherent dynamics in these systems renders a wealth of intriguing phenomena seen in recent experiments such as electron Zeeman frequency focusing, hysteresis, and line dragging. We develop in detail a fully quant…
