An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum Zeno effect and the other using standard methods, is compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase-diffusion.
Conditional pulse nulling (CPN) receiver is proposed by Dolinar to discriminate pulse position modulation (PPM) signals. The receiver using a beam splitter and an on-off photon detector can outperform the standard quantum limit (SQL) for PPM signals. In this paper, we apply this receiver to multi-pulse PPM (MPPM) and binary quantum coding signals, and use dynamic programming algorithm to optimize the control strategy. The MPPM signals is used to improve the band-utilization efficiency, and the binary quantum coding make the communication able to correct the error. Numerical simulation results …
True tripartite entanglement of the state of a system of three qubits can be classified on the basis of stochastic local operations and classical communications (SLOCC). Such states can be classified in two categories: GHZ states and W-states. It is known that GHZ states can be used for teleportation and superdense coding, but the prototype W-state cannot be. However, we show that there is a class of W-states that can be used for perfect teleportation and superdense coding.
We develop a family of perfect quantum error correcting codes that correct for phase errors that arise on any qubit, at any time, during a perfect state transfer experiment. These ensure that we find the optimal operating regime for corrected state transfer. For a specific class of system, we further show that while dephasing noise can be corrected, depolarising noise cannot.
We explicate an example of the so called Task oriented Maximally Entangled states (TMES) in the context of teleportation and superdense coding. In physical situation, this state can emerge from decoherence of more entangled state or may be prepared for the purpose at hand, with less entanglement resource. We find that a variant of the Brown state can be utilized for perfect teleportation of single and two qubit states. In case of superdense coding, it is observed that five cbits can be transmitted by sending only three qubits.
We investigate the usefulness of a recently introduced five qubit state by Brown $\it et al. \normalfont$ \cite{Brown} for quantum teleportation, quantum state sharing and superdense coding. It is shown that this five-qubit state can be utilized for perfect teleportation of arbitrary single and two qubit systems. We devise various schemes for quantum state sharing of an arbitrary single and two particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits…
We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed.
We conjecture that criterion for perfect quantum teleportation is that the Groverian entanglement of the entanglement resource is $1/\sqrt{2}$. In order to examine the validity of our conjecture we analyze the quantum teleportation and superdense coding with $|Φ> = (1/\sqrt{2}) (|00q_1> + |11q_2>)$, where $|q_1>$ and $|q_2>$ are arbitrary normalized single qubit states. It is shown explicitly that $|Φ>$ allows perfect two-party quantum teleportation and superdense coding scenario. Next we compute the Groverian measures for $|ψ>=\sqrt{1/2 - b^2}|100>+b |010>+a|001> +\sqrt{1/2-a^2}|111>$ and $|\…
A quantum key distribution protocol based on time coding uses delayed one photon pulses with minimum time-frequency uncertainty product. Possible overlap between the pulses induces an ambiguous delay measurement and ensures a secure key exchange.
Time coding quantum key distribution with coherent faint pulses is experimentally demonstrated. A measured 3.3 % quantum bit error rate and a relative contrast loss of 8.4 % allow a 0.49 bit/pulse advantage to Bob.
Coherent one photon pulses are sent with four possible time delays with respect to a reference. Ambiguity of the photon time detection resulting from pulses overlap combined with interferometric measurement allows for secure key exchange.
As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and are generalized to multi-particle systems. First we describe two transformations of the shared resources for teleportation and superdense coding, which allow many new protocols from some known ones for that. As an application of these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. As another application,…
We find a protocol transmitting K quantum states crossly in the quantum networks with K pair sender-receiver and one bottleneck channels only with sharing quantum correlations between senders. In these networks senders want to multi cast perfect quantum states to receivers. Perfect send on the quantum networks is impossible just using some additional resources like quantum correlation. This protocol has been used maximum entangled states and Quantum Discord which is best indicator of the quantum nature of the correlation to sharing between senders. At first, to send perfect K states in quantum…
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 letter, 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 p…
A new scheme of quantum key distribution (QKD) using frequency and time coding is proposed, in which the security is based on the frequency-time uncertainty relation. In this scheme, the binary information sequence is encoded randomly on either the central frequency or the time delay at the sender. The central frequency of the single photon pulse is set as omega1 for bit "0" and set as omega2 for bit "1" when frequency coding is selected. While, the single photon pulse is not delayed for bit "0" and is delayed in tao for "1" when time coding is selected. At the receiver, either the frequency o…
We report the security analysis of time-coding quantum key distribution protocols. The protocols make use of coherent single-photon pulses. The key is encoded in the photon time-detection. The use of coherent superposition of states allows to detect eavesdropping of the key. We give a mathematical model of a first protocol from which we derive a second, simpler, protocol. We derive the security analysis of both protocols and find that the secure rates can be similar to those obtained with the BB84 protocol. We then calculate the secure distance for those protocols over standard fibre links. Wh…
We drastically improve the mode overlap between independently seeded, gain-switched laser diodes operating at gigahertz repetition rates by implementing a pulsed light seeding technique. Injecting pulsed light reduces the emission time jitter and enables frequency chirp synchronization while maintaining random optical phases of the emitted laser pulses. We measure interference of these pulsed sources both in the macroscopic regime, where we demonstrate near perfect mode overlap, and in the single photon regime, where we achieve a Hong-Ou-Mandel dip visibility of 0.499+/-0.004, thus saturating …
The necessary and sufficient condition for perfect teleportation and superdense coding and all the suitable states for teleportation and superdense coding
This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More pre…
We have implemented an experimental set-up in order to demonstrate the feasibility of time-coding protocols for quantum key distribution. Alice produces coherent 20 ns faint pulses of light at 853 nm. They are sent to Bob with delay 0 ns (encoding bit 0) or 10 ns (encoding bit 1). Bob directs at random the received pulses to two different arms. In the first one, a 300 ps resolution Si photon-counter allows Bob to precisely measure the detection times of each photon in order to establish the key. Comparing them with the emission times of the pulses sent by Alice allows to evaluate the quantum b…
A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stages of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single-photon while maintaining …
We employ a cascaded system approach to numerically simulate the interaction of photon pulses with a two-level scatterer in a chiral waveguide QED setup. It is possible to expand any pure state of two photons as a superposition of orthogonal two-photon pulses. We show that the scattering of a two-photon pulse of suitable duration may lead to an entangled output state between predominately two equally populated two-photon states. In a complementary wave packet basis, this state is a product state of two orthogonal single photon wave packets. The time reversal of the above scattering process all…
This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly transfer an unknown quantum state from a source subsystem to a target subsystem, where both source and target are formed by ordered sets of some of the nodes. It is proved that a lower bound of the rate at which this quantum communication task is possible is given by the classical min-cut max-flow the…
It is expected that quantum wires (q-wires), will be required to transport quantum information within many quantum computer implementations. Here we describe a new design for a q-wire with perfect transmission using a uniformly coupled Ising spin chain subject to global (homogeneously-applied) pulses. Besides allowing for perfect transport of single qubits, the design also yields the perfect ``mirroring'' of multiply encoded qubits within the wire. We further utilise this global-pulse generated perfect mirror operation as a ``clock cycle'' to perform universal quantum computation on these mult…
In this paper, we study a general linear networked system that contains a tunable memory subsystem; that is, it is decoupled from an optical field for state transportation during the storage process, while it couples to the field during the writing or reading process. The input is given by a single photon state or a coherent state in a pulsed light field. We then completely and explicitly characterize the condition required on the pulse shape achieving the perfect state transfer from the light field to the memory subsystem. The key idea to obtain this result is the use of zero-dynamics princip…
Dynamics of the one-dimensional open Ising chain under influence of $π$ -pulses is studied. It is shown that the application of a specific sequence of such instant kicks to selective spins stimulates arising of perfect dynamical pairwise entanglement between ends of the spin chain. Analytic formulas for the concurrence dynamics are derived. It is also shown that the time required to perfectly entangle the ends of the chains grows linearly with the number of spins in the chain. The final entangled state of the ending spins is always the same and does not depend on length the chain.
A pulse traveling on a uniform nondissipative chain of $N$ masses connected by springs is soon destructured by dispersion. Here it is shown that a proper modulation of the masses and the elastic constants makes it possible to obtain a periodic dynamics and a perfect transmission of any kind of pulse between the chain ends, since the initial configuration evolves to its mirror image in the half period. This makes the chain to behave as a Newton's cradle. By a known algorithm based on orthogonal polynomials one can numerically solve the general inverse problem leading from the spectrum to the dy…
A near perfect, storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell-Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via control Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase matching condition between the data (quantum) and the control (classical) pulses. Herein we discuss the classic…
Quantum communication through spin chains has been extensively investigated. In this scenario, state transfer through linearly arranged spins connected by uniform nearest-neighbor couplings qualifies as a natural choice, with minimal control requirements. However, quantum states usually cannot be perfectly transferred through a uniformly coupled chain due to the dispersion of the chain. Here, we propose an effective quantum control technique to realize almost exact state transfer (AEST) in a quantum spin chain. The strategy is to add a leakage elimination operator (LEO) Hamiltonian to the evol…
Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to realize quantum dense coding \textit{via} entanglement swapping in a cavity array containing a certain number of two-level atoms. Proper choice of system parameters such as atom-cavity couplings and inter-cavity couplings allows perfect transfer of information. A high fidelity transfer of information is shown to be possible by using recently achieved experi…
We describe novel composite pulse sequences which act as general rotors and thus are suitable for nuclear magnetic resonance (NMR) quantum computation. The Resonance Offset Tailoring To Enhance Nutations (ROTTEN) approach permits perfect compensation of off-resonance errors at two selected frequencies placed symmetrically around the frequency of the RF source.
The recently proposed Universal Blind Quantum Computation (UBQC) protocol allows a client to perform an arbitrary quantum computation on a remote server such that perfect privacy is guaranteed if the client is capable of producing random separable single qubit states. While from a theoretical point of view, this arguably constitutes the lowest possible quantum requirement, from a pragmatic point of view, generation of random single qubits which can be sent along long distances without loss is quite challenging and can never be achieved perfectly. In analogy to the concept of approximate securi…
We report the first experimental realization of perfect W-state in a superconducting qubit based system. In contrast to maximally entangled state, the perfect W state is different in weights and phases of the terms contained in the maximally entangled W-state. The prefect W state finds important applications in quantum information processing tasks such as perfect teleportation, superdense coding, secret sharing etc. The efficiency of generation is quantified by fidelity which is calculated by performing full quantum state tomography. To verify the presence of genuine nonlocality in the generat…
Using an exactly solvable pure dephasing model, we show how entanglement between qubits can be generated via the interaction with a common environment and concurrent application of suitable control pulses. The control pulses are able to effectively remove the detrimental effect of the environment while preserving the indirect interaction between the qubits, thereby leading to the generation of near-perfect entanglement. Furthermore, we also investigate the entanglement dynamics if the qubits are directly interacting; this interaction may even contain a noise term. The present of this additiona…
Quantum repeater networks have attracted attention for the implementation of long-distance and large-scale sharing of quantum states. Recently, researchers extended classical network coding, which is a technique for throughput enhancement, into quantum information. The utility of quantum network coding (QNC) has been shown under ideal conditions, but it has not been studied previously under conditions of noise and shortage of quantum resources. We analyzed QNC on a butterfly network, which can create end-to-end Bell pairs at twice the rate of the standard quantum network repeater approach. The…
We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to $ε^4$, while the phase error is proportional to $ε$, where $ε$ is the characteristic deviation from the perfect pulse duration.
Based on the concept of many-letter theory, an observable is defined measuring the raw quantum information content of single messages. A general characterization of quantum codes using the Kraus representation is given. Compression codes are defined by their property of decreasing the expected raw information content of a given message ensemble. Lossless quantum codes, in contrast to lossy codes, provide the retrieval of the original data with perfect fidelity. A general lossless coding scheme is given that translates between two quantum alphabets. It is shown that this scheme is never compres…
We address the question of existence of private quantum channel for qubits encoded in polarization degrees of freedom of a photon, that remains secure even if multi-photon (instead of single-photon) pulse is emitted. We show that random unitary channel distributed according to SU(2) Haar measure has this property. Further we analyze the qubit unitary k-designs. We show they ensure security if the photons' parity of the source is guaranteed. Otherwise, the qubit unitary k-designs do not guarantee perfect security.
We propose a method to deterministically prepare a desired quantum state in a one-dimensional (1D) continuum by a shaped photon pulse. This method is based on time-reverse of the quantum emission process. We show that the desired quantum state such as Dicke or timed-Dicke state can be successfully prepared with very high fidelity even if the dissipation to the environment is nonnegligible and the pulse shaping is not perfect. We also show that large quantum entanglement between emitters can be created by just a single photon pulse. This method is experimentally feasible in 1D waveguide-QED or …
We demonstrate that perfect state transfer can be achieved using an engineered spin chain and clean local end-chain operations, without requiring the initialization of the state of the medium nor fine tuning of control-pulses. This considerably relaxes the prerequisites for obtaining reliable transfer of quantum information across interacting-spin systems. Moreover, it allows us to shed light on the interplay among purity, entanglement and operations on a class of many-body systems potentially useful for quantum information processing tasks.
Distributing quantum state and entanglement between distant nodes is a crucial task in distributed quantum information processing on large-scale quantum networks. Quantum network coding provides an alternative solution for quantum state distribution especially when the bottleneck problems must be considered and high communication speed is required. Here, we report the first experimental realization of quantum network coding on the butterfly network. With the help of prior entanglements shared between senders, two quantum states can be crossly transmitted perfectly through the butterfly network…
Interference of laser pulses is an essential ingredient of quantum randomness; therefore, probabilistic properties of laser pulses gains new relevance. Here, we consider in detail the combined influence of the three effects - chirp, jitter and relaxation oscillations - on the probability density function of the interference of pulses from a gain-switched semiconductor laser. We develop a rigorous model based on laser rate equations and demonstrate that only consideration of all these three effects together allows describing the interference statistics properly. We supplement our theoretical ca…
A method for time differentiation based on a Babinet-Soleil-Bravais compensator is introduced. The complex transfer function of the device is measured using polarization spectral interferometry. Time differentiation of both the pulse field and pulse envelope are demonstrated over a spectral width of about 100 THz with a measured overlap with the objective mode greater than 99.8%. This pulse shaping technique is shown to be perfectly suited to time metrology at the quantum limit.
The Sauter-Schwinger process of electron-positron pair creation from vacuum, driven by a sequence of time-dependent electric-field pulses, is studied in the framework of quantum-field theoretical approach. As demonstrated by our numerical results, the probability distributions of produced pairs exhibit intra- and inter-pulse interference structures. We show that such structures can be observed beyond the regime of applicability of the WKB theory, which was the focus of earlier investigations. Going beyond these developments, we perform the analysis of the time-evolution operator for an arbitra…
Analytic mass-spring chains with dispersionless pulse transfer and fractional revival are presented. These are obtained using the properties of the para-Racah polynomials. This provides classical analogs of the quantum spin chains that realize important tasks in quantum information: perfect state transfer and entanglement generation.
X-ray free-electron lasers (FEL) deliver ultrabright X-ray pulses, but not the sequences of phase-coherent pulses required for time-domain interferometry and control of quantum states. For conventional split-and-delay schemes to produce such sequences the challenge stems from extreme stability requirements when splitting Angstrom wavelength beams where tiniest path length differences introduce phase jitter. We describe an FEL mode based on selective electron bunch degradation and transverse beam shaping in the accelerator, combined with a self-seeded photon emission scheme. Instead of splittin…
The k-pair problem in network coding theory asks to send k messages simultaneously between k source-target pairs over a directed acyclic graph. In a previous paper [ICALP 2009, Part I, pages 622--633] the present authors showed that if a classical k-pair problem is solvable by means of a linear coding scheme, then the quantum k-pair problem over the same graph is also solvable, provided that classical communication can be sent for free between any pair of nodes of the graph. Here we address the main case that remained open in our previous work, namely whether nonlinear classical network coding…
