Frequency Degrees Of Freedom Research Articles

Analysis of Secret Key Randomness Exploiting the Radio Channel Variability

A few years ago, physical layer based techniques have started to be considered as a way to improve security in wireless communications. A well known problem is the management of ciphering keys, both regarding the generation and distribution of these keys. A way to alleviate such difficulties is to use a common source of randomness for the legitimate terminals, not accessible to an eavesdropper. This is the case of the fading propagation channel, when exact or approximate reciprocity applies. Although this principle has been known for long, not so many works have evaluated the effect of radio channel properties in practical environments on the degree of randomness of the generated keys. To this end, we here investigate indoor radio channel measurements in different environments and settings at either 2.4625 GHz or 5.4 GHz band, of particular interest for WIFI related standards. Key bits are extracted by quantizing the complex channel coefficients and their randomness is evaluated using the NIST test suite. We then look at the impact of the carrier frequency, the channel variability in the space, time, and frequency degrees of freedom used to construct a long secret key, in relation to the nature of the radio environment such as the LOS/NLOS character.

Hyper-parallel photonic quantum computation and manipulation on hyperentangled states

Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.

Efficient preparation of Greenberger–Horne–Zeilinger state and W state of atoms with the help of the controlled phase flip gates in quantum nodes connected by collective-noise channels

Noise plays a troublesome role for entanglement generation, because the polarization entanglement of photons can be easily disturbed by the noise. In this paper, we propose a protocol to prepare Greenberger–Horne–Zeilinger state and W state of atoms in quantum nodes connected by collective-noise channels assisted by quantum nondemolition detectors (QNDs) and the controlled phase flip gates. The frequency degrees of freedom are exploited in our protocol. The successful probability of our protocol can reach 100% neglecting the photon loss and assuming that the efficiency of QNDs is 1. Moreover, the number of times of using QNDs is limited, and this makes the protocol quite effective when collective noise is small.

Complete N-Qubit Greenberger—Horne—Zeilinger States Analysis Assisted by Frequency Degree of Freedom

We present an efficient and simple protocol to unambiguously distinguish 2N mutual orthogonal N-qubit Greenberger—Horne—Zeilinger states in polarization degree of freedom assisted by the frequency one. This scheme is based on N single photon Bell state measurements, which can be implemented non-locally. The success probability is 100% in principle and our scheme is feasible with current technology. All the advantages make our protocol meaningful and practical in quantum information processing.

Complete hyperentanglement-assisted multi-photon Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity

We propose a feasible and efficient scheme to complete hyperentanglement-assisted multi-photon Greenberger–Horne–Zeilinger (GHZ) states analysis with the quantum nondemolition detectors (QNDs). Firstly, we unambiguously distinguish the two-photon Bell states and three-photon GHZ states in polarization degree of freedom (DOF) assisted with the frequency DOF. Then, we show that the scheme can be extended to the N-photon (N>3) GHZ states in polarization DOF analysis, and moreover, the entanglement in polarization DOF is not disturbed by our operations. All these advantages make this scheme more meaningful in quantum information processing.

Deterministic Frequency-Based Polarization Entanglement Concentration with the Multipartite Less-Hyperentangled State

A deterministic entanglement concentration protocol (ECP) is demonstrated in a multipartite less-hyperentangled system, containing the simultaneous entanglements in polarization and frequency degrees of freedom. The motivation is that the entangled system in frequency degree of freedom suffers little from the effects of the channel noise in optical fibers. Consequently, a maximally entangled system can be generated in polarization degree of freedom from the multipartite less-hyperentangled system with cross-Kerr nonlinearity. Compared with the conventional ECPs that have success probabilities less than one while iterating their recursive entanglement concentration processes several times to achieve a maximally entangled system in polarization degree of freedom, the present ECP can generate a maximally entangled system in polarization degree of freedom in two steps with a certainty. It may be useful for enhancing the efficiency of communications in long-distance quantum computation networks.

Complete Bell-state analysis for a single-photon hybrid entangled state

We propose a scheme capable of performing complete Bell-state analysis for a single-photon hybrid entangled state. Our single-photon state is encoded in both polarization and frequency degrees of freedom. The setup of the scheme is composed of polarizing beam splitters, half wave plates, frequency shifters, and independent wavelength division multiplexers, which are feasible using current technology. We also show that with this setup we can perform complete two-photon Bell-state analysis schemes for polarization degrees of freedom. Moreover, it can also be used to perform the teleportation scheme between different degrees of freedom. This setup may allow extensive applications in current quantum communications.

Deterministic Tripartite Entanglement Distributions of the W State over Collective-Noise Channels

A deterministic entanglement distribution protocol (EDP) is proposed in principle for transmitting a maximally entangled W state over collective-noise channels. Using this EDP, a W state can be reconstructed directly from a three-photon entangled state in the frequency degree of freedom prepared among three remote participants due to the fact that it suffers little from the channel noise. In essence, it is a entanglement transformation between different degrees of freedom in three-photon entangled system. This EDP adopts the cross-Kerr nonlinearity media to complete the task of the single-photon detections, which can increase the efficiency of entanglement distribution since it does not require the sophisticated single-photon detectors for the usual measurements and the retained photons can be still held solely by three respective participants after entanglement distillation.

POLARIZATION ENTANGLEMENT CONCENTRATIONS WITH LESS-HYPERENTANGLED PHOTON PAIRS IN MULTIPLE DEGREES OF FREEDOM

We demonstrate two entanglement concentration protocols (ECPs) for photon pairs in less-hyperentanglement, the simultaneous entanglement in multiple degrees of freedom. Using these ECPs, some maximally entangled states in polarization can be reconstructed deterministically from less-hyperentangled ones shared between remote participants. Both of the success probabilities are 100% in principle, and they do not require additional single photons. The former is implemented with the passive linear optics, which is achievable with current technology. The later adopts the cross-Kerr nonlinearity media to complete this task, which can increase the efficiency of the entanglement concentration process since it does not require the sophisticated single-photon detectors for measurements. The two ECPs are useful for practical long-distance quantum communication due to the fact that the entangled state in either the spatial degree of freedom or the frequency degree of freedom suffers little from channel noise in optical fiber.

Quantum superdense coding based on hyperentanglement

We present a scheme for quantum superdense coding with hyperentanglement, in which the sender can transfer four bits of classical information by sending only one photon. The important device in the scheme is the hyperentangled Bell-state analyzer in both polarization and frequency degrees of freedom, which is also constructed in the paper by using a quantum nondemolition detector assisted by cross-Kerr nonlinearity. Our scheme can transfer more information with less resources than the existing schemes and is nearly deterministic and nondestructive.

Efficient W polarization state distribution over an arbitrary collective-noise channel with cross-Kerr nonlinearity

We propose an efficient protocol for W polarization entangled state distribution over an arbitrary collective-noise channel with the help of the cross-Kerr nonlinearity. The entangled state in the frequency degree of freedom, which suffers little from the noise in an optical fiber, is used in the present protocol. The frequency entanglement can be transferred into polarization entanglement with the success probability of 100%. So, the three parities can share the maximally W polarization state with local operations and polarization independent wavelength division multiplexers which can erase distinguishability for frequency.

Efficient quantum entanglement distribution over an arbitrary collective-noise channel

We present an efficient quantum entanglement distribution over an arbitrary collective-noise channel. The basic idea in the present scheme is that two parties in quantum communication first transmit the entangled states in the frequency degree of freedom which suffers little from the noise in an optical fiber. After the two parties share the photon pairs, they add some operations and equipments to transfer the frequency entanglement of pairs into the polarization entanglement with the success probability of 100\%. Finally, they can get maximally entangled polarization states with polarization independent wavelength division multiplexers and quantum frequency up-conversion which can erase distinguishability for frequency. Compared with conventional entanglement purification protocols, the present scheme works in a deterministic way in principle. Surprisingly, the collective noise leads to an additional advantage.

Efficient faithful qubit transmission with frequency degree of freedom

We propose an efficient faithful polarization-state transmission scheme by utilizing frequency degree of freedom besides polarization and an additional qubit prepared in a fixed polarization. An arbitrary single-photon polarization state is protected against the collective noise probabilistically. With the help of frequency beam splitter and frequency shifter, the success probability of our faithful qubit transmission scheme with frequency degree of freedom can be 1/2 in principle.

Energy transfer rates in inhomogeneous van der Waals clusters

The internal energy exchanges inside an inhomogeneous van der Waals cluster are investigated by means of molecular dynamic calculations. The very long time scales for relaxation of the high frequency degrees of freedom are examined within the framework of Nekhoroshev's theorem.

List of contributors

We propose a feasible and efficient scheme to complete hyperentanglement-assisted multi-photon Greenberger–Horne–Zeilinger (GHZ) states analysis with the quantum nondemolition detectors (QNDs). Firstly, we unambiguously distinguish the two-photon Bell states and three-photon GHZ states in polarization degree of freedom (DOF) assisted with the frequency DOF. Then, we show that the scheme can be extended to the N-photon (N>3) GHZ states in polarization DOF analysis, and moreover, the entanglement in polarization DOF is not disturbed by our operations. All these advantages make this scheme more meaningful in quantum information processing.