Elementary quantum gates with Gaussian states

We study the question of converting initially Gaussian states into non-Gaussian ones by two- and three-photon subtraction to improve non-classical properties of the conditional optical fields. We show the photon subtraction may effectively generate non-Gaussian states only in case of small values of the mean values of the position and momentum operators. In particular, the photon-subtracted state can be made arbitrary close to Gaussian state in limiting case of large initial amplitude of displacement. Use of initial displacement in input Gaussian states opens wider prospects to manipulate them. In particular, realization of probabilistic Hadamard gate with input Gaussian states is discussed where photon subtraction is motive force able unevenly to increase measure of non-classicality of the output state. Subtraction of larger number of photons enables to increase fidelity and non-classical measure of the conditional states.     

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 (\(\alpha \)-representation) by multiplying the transposed transformation matrix on a column vector of initial state. Analytical expressions of the \(\alpha \)-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.     

Two-mode Gaussian product states in a lossy interferometer

The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer–Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number is compared to the shot noise-limited scaling for dual squeezed vacuum states and dual squeezed, displaced vacuum states.     

Number state filtered coherent states

Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the negativity of the Wigner function and the entanglement potential. Filtering of the vacuum from a coherent state is almost like the photon addition. However, filtering makes the state more resilient against dissipation than photon addition. Vacuum state filtered coherent states perform better than the photon-added coherent states for a two-way quantum key distribution protocol. A scheme to generate these states in multi-photon atom–field interaction is presented.     

Generating multi-mode entangled coherent W and GHZ states via optical system based fusion mechanism

Fusion technology has been demonstrated to be a good method for generating a large-scale entangled coherent W or GHZ state from two small ones in QED system. It is of importance to study how to fuse small-scale entangled coherent W or GHZ states via optical system. In this paper, we present a scheme for generating larger entangled coherent W or GHZ state in an optical system by virtue of fusion technology. The key fusion mechanism is realized by photon detectors and a Mach–Zehnder interferometer with its two arms immersed in Kerr media, by which an n-mode entangled coherent W state and an m-mode entangled coherent W state can be probabilistically fused into an (\(n+m-2\))-mode entangled coherent W state. This fusion scheme applies to entangled coherent GHZ state too but with a unit probability of success. Feasibility analysis indicates that our fusion scheme may be realized with current experimental technology. Large-scale entangled coherent W and GHZ states may find new applications in quantum communication.     

Quantum computation and entangled state generation via long-range off-resonant Raman coupling

A scheme is proposed to implement two-qubit controlled quantum phase gate and SWAP gate and generate two-qubit entangled state via long-range off-resonant Raman coupling between two spatially separated superconducting quantum-interference devices (SQUIDs). In the scheme each SQUID is coupled with a single-mode cavity individually and the two distant cavities are connected by an optical fiber. The two lowest levels of each SQUID are used to represent the two logical states of a qubit while the two intermediate levels of each SQUID are used to facilitate coherent coupling of quantum states of the qubits during the virtual excitation process of photon. The scheme is robust against fiber loss, cavity decay, and the effect of spontaneous decay from the higher levels and it would be an important step toward distributed quantum computation and long-distance entanglement distribution.     

Two-way QKD with single-photon-added coherent states

In this work we present a two-way quantum key distribution (QKD) scheme that uses single-photon-added coherent states and displacement operations. The first party randomly sends coherent states (CS) or single-photon-added coherent states (SPACS) to the second party. The latter sends back the same state it received. Both parties decide which kind of states they are receiving by detecting or not a photon on the received signal after displacement operations. The first party must determine whether its sent and received states are equal; otherwise, the case must be discarded. We are going to show that an eavesdropper provided with a beam splitter gets the same information in any of the non-discarded cases. The key can be obtained by assigning 0 to CS and 1 to SPACS in the non-discarded cases. This protocol guarantees keys’ security in the presence of a beam splitter attack even for states with a high number of photons in the sent signal. It also works in a lossy quantum channel, becoming a good bet for improving long-distance QKD.     

Entangled photon-added coherent states

We study the degree of entanglement of arbitrary superpositions of m, n photon-added coherent states (PACS) \(\mathinner {|{\psi }\rangle } \propto u \mathinner {|{{\alpha },m}\rangle }\mathinner {|{{\beta },n }\rangle }+ v \mathinner {|{{\beta },n}\rangle }\mathinner {|{{\alpha },m}\rangle }\) using the concurrence and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: \(\mathinner {|{\psi }\rangle } \propto \mathinner {|{\alpha }\rangle }_a\mathinner {|{-\alpha }\rangle }_b + \mathinner {|{-\alpha }\rangle }_a\mathinner {|{\alpha }\rangle }_b \) whose entanglement tends to zero for \(\alpha \rightarrow 0\), can be maximal if al least one photon is added in a subsystem. A full family of maximally entangled PACS is also presented. We also analyzed the decoherence effects in the entangled PACS induced by a simple depolarizing channel . We find that robustness against depolarization is increased by adding photons to the coherent states of the superposition. We obtain the dependence of the critical depolarization \(p_{\text {crit}}\) for null entanglement as a function of \(m,n, \alpha \) and \(\beta \).     

Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement

In this paper, a scheme for N-photon Greenberger–Horne–Zeilinger (GHZ) state analysis using hyperentangled states in multiple degrees of freedom with only linear optics and single photon detectors is proposed. The photons are separated and processed in different processing units. All the eight GHZ-states in either the polarization or the momentum degree of freedom can be completely distinguished. The scheme is implementable using present-day technology.     

A Concise Guide to Complex Hadamard Matrices

Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12,14 and 16, which we could not find in the existing literature.     

Generation of entangled coherent-squeezed states: their entanglement and nonclassical properties

In this paper, after a brief review on the coherent states and squeezed states, we introduce two classes of entangled coherent-squeezed states. Next, in order to generate the introduced entangled states, we present a theoretical scheme based on the resonant atom-field interaction. In the proposed model, a \(\varLambda \)-type three-level atom interacts with a two-mode quantized field in the presence of two strong classical fields. Then, we study the amount of entanglement of the generated entangled states using the concurrence and linear entropy. Moreover, we evaluate a few of their nonclassical properties such as photon statistics, second-order correlation function, and quadrature squeezing and establish their nonclassicality features.     

Enlarge the scale of W state by connecting multiple existed W states

We propose a simple scheme to generate large-scale W state. With the cross-phase modulation, we design a photon number resolving discrimination. This discrimination, associated with some single-photon operations, is enough to connect the existed W states. No more two-photon or multi-photon operations are required. This scheme is powerful and flexible for connecting arbitrary number of W states. It is therefore suitable for creating large-scale W state with the current technology.     

Coherence of one-dimensional quantum walk on cycles

Quantum coherence plays a central role in quantum mechanics and provides essential power for quantum information processing. In this paper, we study the dynamics of the \(l_1\) norm coherence in one-dimensional quantum walk on cycles for two initial states. For the first initial state, the walker starts from a single position. The coherence increases with the number of steps at the beginning and then fluctuates over time after approaching to saturation. The coherence with odd number of sites is much larger than that with even number of sites. Another initial state, i.e., the equally superposition state, is also considered. The coherence of the whole system is proved to be \(N-1\) (\(2N-1\)) for any odd (even) time step where N is the number of sites. We also investigate the influence of two unitary noises, i.e., noisy Hadamard operator and broken link, on the coherence evolution.     

Generating multi-photon W-like states for perfect quantum teleportation and superdense coding

An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this paper, we propose a simple optical scheme for efficient preparation of large-scale polarization-based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla photon. Our scheme can also generate large-scale W states by fusing or expanding W or even W-like states. The cost analysis shows that in generating large-scale W states, the fusion mechanism achieves a higher efficiency with non-maximally entangled W-like states than maximally entangled W states. Our scheme can also start fusion or expansion with Bell states, and it is composed of a polarization-dependent beam splitter, two polarizing beam splitters and photon detectors. Requiring no ancilla photon or controlled gate to operate, our scheme can be realized with the current photonics technology and we believe it enable advances in quantum teleportation and superdense coding in multipartite settings.     

Semi-quantum information splitting using GHZ-type states

By using a generalized Greenberger–Horne–Zeilinger (GHZ) state in which is locally unitarily connected with standard GHZ state as a communication channel, semi-quantum key distribution is extended to study semi-quantum information splitting protocols for secret sharing of quantum information. In our scheme, quantum Alice splits arbitrary two, three and N-qubit states with two classical parties, Bob and Charlie, in a way that both parties are sufficient to reconstruct Alice’s original states only under the condition of which she/he obtains the help from another one, but one of them cannot. The presented protocols are helpful for both secure against certain eavesdropping attacks and economical in processing of quantum information.     

Quantum splitting an arbitrary three-qubit state with χ-state

In this paper, we propose two schemes to remotely split an arbitrary three-qubit state. The χ and a GHZ state are used to construct the quantum channel. One scheme is completed by using the generalized Bell basis measurement of multi-particles. The other scheme is constructed by using the quantum primitives, which are described by the quantum circuit and photon architecture.     

Two-mode squeezing operator in circuit QED

We theoretically investigate the implementation of the two-mode squeezing operator in circuit quantum electrodynamics. Inspired by a previous scheme for optical cavities (Prado et al. in Phys Rev A 73:043803, 2006), we employ a superconducting qubit coupled to two nondegenerate quantum modes and use a driving field on the qubit to adequately control the resonator–qubit interaction. Based on the generation of two-mode squeezed vacuum states, firstly we analyze the validity of our model in the ideal situation and then we investigate the influence of the dissipation mechanisms on the generation of the two-mode squeezing operation, namely the qubit and resonator mode decays and qubit dephasing. We show that our scheme allows the generation of highly squeezed states even with the state-of-the-art parameters, leading to a theoretical prediction of more than 10 dB of two-mode squeezing. Furthermore, our protocol is able to squeeze an arbitrary initial state of the resonators, which makes our scheme attractive for future applications in continuous-variable quantum information processing and quantum metrology in the realm of circuit quantum electrodynamics.     

An efficient scheme for multi-party quantum state sharing of an arbitrary multi-qubit state with one GHZ channel

We present an innovative and extremely efficient scheme to share an arbitrary multi-qubit state between n agents with only 1 GHZ channel under control of m agents in a network. Compared with existing ones in this literature, our scheme requires less communication resources, least qubits and only three physical favorable simple operations (single-qubit measurement, Bell-basis measurement and CNOT gate operations) are included, leading to a higher overall efficiency.     

Quantum interference of photons in simple networks

A theoretical investigation of quantum interference of photonic multistates in simple devices like beam splitters, Mach–Zehnder interferometers and double-loop devices are presented. Variable transmission and reflection coefficients as well as variable phase shifts are included in order to calculate quantum states and mean photon numbers at the outputs. Various input states like Fock states and coherent states and a combination of both are considered as well as squeezed states. Two methods are applied: The direct matrix method and the method of unitary representation. Remarkable results appear in a double-loop interferometer where for special phase shifts equal mean photon numbers in the three output ports are obtained provided certain input states are given. A computerized simulation of general networks using various input Fock states is presented. Multistate devices will be used in future linear quantum computation and quantum information processing schemes.     

Quantum state sharing against the controller’s cheating

Most existing QSTS schemes are equivalent to the controlled teleportation, in which a designated agent (i.e., the recoverer) can recover the teleported state with the help of the controllers. However, the controller may attempt to cheat the recoverer during the phase of recovering the secret state. How can we detect this cheating? In this paper, we considered the problem of detecting the controller’s cheating in Quantum State Sharing, and further proposed an effective Quantum State Sharing scheme against the controller’s cheating. We cleverly use Quantum Secret Sharing, Multiple Quantum States Sharing and decoy-particle techniques. In our scheme, via a previously shared entanglement state Alice can teleport multiple arbitrary multi-qubit states to Bob with the help of Charlie. Furthermore, by the classical information shared previously, Alice and Bob can check whether there is any cheating of Charlie. In addition, our scheme only needs to perform Bell-state and single-particle measurements, and to apply C-NOT gate and other single-particle unitary operations. With the present techniques, it is feasible to implement these necessary measurements and operations.