Showing papers on "Quantum channel published in 2008"

The quantum internet

Abstract: Quantum networks provide opportunities and challenges across a range of intellectual and technical frontiers, including quantum computation, communication and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for generating and characterizing quantum coherence and entanglement. Fundamental to this endeavour are quantum interconnects, which convert quantum states from one physical system to those of another in a reversible manner. Such quantum connectivity in networks can be achieved by the optical interactions of single photons and atoms, allowing the distribution of entanglement across the network and the teleportation of quantum states between nodes.

Quantum Discord and the Power of One Qubit

Abstract: We use quantum discord to characterize the correlations present in the model called deterministic quantum computation with one quantum bit (DQC1), introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. The initial state, operations, and measurements in the model all point to a natural bipartite split between the control qubit and the mixed ones. Although there is no entanglement between these two parts, we show that the quantum discord across this split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model.

Quantum discord for two-qubit systems

Abstract: Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.

Experimental quantum computing without entanglement.

Abstract: Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.

Assessing non-Markovian quantum dynamics.

Abstract: We investigate what a snapshot of a quantum evolution--a quantum channel reflecting open system dynamics--reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of "Markovianity" is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.

Experimental demonstration of a BDCZ quantum repeater node.

Abstract: At distances beyond about 100 km, quantum communication fails due to photon losses in the transmission channel. To overcome this problem, Briegel, Dur, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Their implementation has proved challenging due to the difficulty of integrating a quantum memory. Zhen-ShengYuan et al. realize a building block of the BDCZ quantum repeater, demonstrating entanglement swapping with storage and retrieval of light from atomic quantum memories. Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication1,2,3,4 (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails5 when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dur, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters6, combining entanglement swapping7 and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated8, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme9,10 that incorporates the strategy of BDCZ with atomic quantum memories11. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.

$H^{\infty}$ Control of Linear Quantum Stochastic Systems

Abstract: The purpose of this paper is to formulate and solve a H infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived. This enables a quantum version of the two Riccati solution to the H infin control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.

Solid-state quantum memory using the 31 P nuclear spin

Abstract: The transfer of information between the entities that do the processing and memory is crucial — and problematic — for quantum computation. In classical systems the information transfer can include a copying step, where errors can be spotted and corrected, but in quantum systems copying is fundamentally precluded. Morton et al. demonstrate a technology that could solve the problem: the coherent storage and readout of information between electron-spin processing elements and memory elements based on a nuclear spin. The system utilizes phosphorus-31 spin donors in a silicon-28 crystal. The nuclear spin acts as a memory element that can faithfully store the full state of the electron spin for more than a second, then transfer it back to the electron spin with about 90% efficiency. The transfer of information between processing entities and memory is crucial for quantum computation; it is challenging because the process must remain coherent at all times to preserve the quantum nature of the information. This paper demonstrates coherent storage and readout of information between electron-spin processing elements and memory elements based on a nuclear spin. The transfer of information between different physical forms—for example processing entities and memory—is a central theme in communication and computation. This is crucial in quantum computation1, where great effort2 must be taken to protect the integrity of a fragile quantum bit (qubit). However, transfer of quantum information is particularly challenging, as the process must remain coherent at all times to preserve the quantum nature of the information3. Here we demonstrate the coherent transfer of a superposition state in an electron-spin ‘processing’ qubit to a nuclear-spin ‘memory’ qubit, using a combination of microwave and radio-frequency pulses applied to 31P donors in an isotopically pure 28Si crystal4,5. The state is left in the nuclear spin on a timescale that is long compared with the electron decoherence time, and is then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store–readout fidelity is about 90 per cent, with the loss attributed to imperfect rotations, and can be improved through the use of composite pulses6. The coherence lifetime of the quantum memory element at 5.5 K exceeds 1 s.

Quantum communication with zero-capacity channels.

Abstract: Communication over a noisy quantum channel introduces errors in the transmission that must be corrected. A fundamental bound on quantum error correction is the quantum capacity, which quantifies the amount of quantum data that can be protected. We show theoretically that two quantum channels, each with a transmission capacity of zero, can have a nonzero capacity when used together. This unveils a rich structure in the theory of quantum communications, implying that the quantum capacity does not completely specify a channel's ability to transmit quantum information.

Perfect Teleportation, Quantum state sharing and Superdense Coding through a Genuinely Entangled Five-qubit State

Abstract: We investigate the usefulness of a recently introduced five qubit state by Brown $\it et al. ormalfont$ \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.

Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

Abstract: We present a theoretical study of a superconducting charge qubit dispersively coupled to a transmission line resonator. Starting from a master equation description of this coupled system and using a polaron transformation, we obtain an exact effective master equation for the qubit. We then use quantum trajectory theory to investigate the measurement of the qubit by continuous homodyne measurement of the resonator out field. Using the same polaron transformation, a stochastic master equation for the conditional state of the qubit is obtained. From this result, various definitions of the measurement time are studied. Furthermore, we find that in the limit of strong homodyne measurement, typical quantum trajectories for the qubit exhibit a crossover from diffusive to jumplike behavior. Finally, in the presence of Rabi drive on the qubit, the qubit dynamics is shown to exhibit quantum Zeno behavior.

Continuous-variable quantum cryptography using two-way quantum communication

Abstract: A class of quantum-cryptographic protocols is proposed that involves back-and-forth communication between two parties. The approach is shown to provide enhanced security and should tolerate higher levels of noise and loss than conventional ‘one-way’ protocols.

A Resource Framework for Quantum Shannon Theory

Abstract: Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper, we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless.

Reversal of the Weak Measurement of a Quantum State in a Superconducting Phase Qubit

Abstract: We demonstrate in a superconducting qubit the conditional recovery (uncollapsing) of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a nonunitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.

Experimental verification of the feasibility of a quantum channel between space and Earth

Abstract: Extending quantum communication to space environments would enable us to perform fundamental experiments on quantum physics as well as applications of quantum information at planetary and interplanetary scales Here, we report on the first experimental study of the conditions for the implementation of the single-photon exchange between a satellite and an Earth-based station We built an experiment that mimics a single photon source on a satellite, exploiting the telescope at the Matera Laser Ranging Observatory of the Italian Space Agency to detect the transmitted photons Weak laser pulses, emitted by the ground-based station, are directed toward a satellite equipped with cube-corner retroreflectors These reflect a small portion of the pulse, with an average of less- than-one photon per pulse directed to our receiver, as required for faint-pulse

Memory-built-in quantum teleportation with photonic and atomic qubits

Abstract: The combination of quantum teleportation1 and quantum memory2,3,4,5 of photonic qubits is essential for future implementations of large-scale quantum communication6 and measurement-based quantum computation7,8. Both steps have been achieved separately in many proof-of-principle experiments9,10,11,12,13,14, but the demonstration of memory-built-in teleportation of photonic qubits remains an experimental challenge. Here, we demonstrate teleportation between photonic (flying) and atomic (stationary) qubits. In our experiment, an unknown polarization state of a single photon is teleported over 7 m onto a remote atomic qubit that also serves as a quantum memory. The teleported state can be stored and successfully read out for up to 8 μs. Besides being of fundamental interest, teleportation between photonic and atomic qubits with the direct inclusion of a readable quantum memory represents a step towards an efficient and scalable quantum network2,3,4,5,6,7,8.

Joint remote state preparation

Abstract: Alice, Bob and Charlie are three remote parties Alice and Bob share the classical knowledge of a secret qubit state We consider the following question: 'how can Alice and Bob jointly prepare the qubit state for Charlie?' Two different protocols are proposed for such a joint remote state preparation The first protocol uses a single GHZ state while the second one uses a pair of EPR states as the quantum channel whose entanglement is not necessarily maximal

Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1

Abstract: For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p > 1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p = 1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.

Memory effects in quantum channel discrimination

Abstract: We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory, based on the general theory of quantum testers. For discrimination and estimation of sets of independent unitary channels, we prove optimality of parallel protocols among all possible architectures.

A fibre bundle over manifolds of quantum channels and its application to quantum statistics

Abstract: A fibre bundle structure is introduced over manifolds of quantum channels. This structure has a close connection with the problem of estimating an unknown quantum channel ?? specified by a parameter ?. It is shown that the quantum Fisher information of the family of output states maximized over all input states , which quantifies the ultimate statistical distinguishability of the parameter ?, is expressed in terms of a geometrical quantity on the fibre bundle. Using this formula, a criterion for the maximum quantum Fisher information of the nth extended channel (id ? ??)?n to be O(n) is derived. This criterion further proves that for almost all quantum channels, the maximum quantum Fisher information increases in the order of O(n).

Asymptotic teleportation scheme as a universal programmable quantum processor.

Abstract: We consider a scheme of quantum teleportation where a receiver has multiple (N) output ports and obtains the teleported state by merely selecting one of the N ports according to the outcome of the sender's measurement. We demonstrate that such teleportation is possible by showing an explicit protocol where N pairs of maximally entangled qubits are employed. The optimal measurement performed by a sender is the square-root measurement, and a perfect teleportation fidelity is asymptotically achieved for a large N limit. Such asymptotic teleportation can be utilized as a universal programmable processor.

Manipulating biphotonic qutrits

Abstract: Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.

Entanglement-Assisted Capacity of Quantum Multiple-Access Channels

Abstract: We find a regularized formula for the entanglement-assisted (EA) capacity region for quantum multiple-access channels (QMAC). We illustrate the capacity region calculation with the example of the collective phase-flip channel which admits a single-letter characterization. On the way, we provide a first-principles proof of the EA coding theorem based on a packing argument. We observe that the Holevo-Schumacher-Westmoreland theorem may be obtained from a modification of our EA protocol. We remark on the existence of a family hierarchy of protocols for multiparty scenarios with a single receiver, in analogy to the two-party case. In this way, we relate several previous results regarding QMACs.

Fidelity and quantum phase transitions

Abstract: It is shown that the fidelity, a basic notion of quantum information science, may be used to characterize quantum phase transitions, regardless of what type of internal order is present in quantum many-body states. The equivalence between the existence of an order parameter and the orthogonality of different ground-state wavefunctions for a system undergoing a quantum phase transition is used to justify the introduction of the notions of irrelevant and relevant information as the counterparts of fluctuations and orders in the conventional description. The irrelevant and relevant information are quantified, which allows us to identify unstable and stable fixed points (in the sense of renormalization group theory) for quantum spin chains.

Capacity theorems for quantum multiple-access channels: classical-quantum and quantum-quantum capacity regions

Abstract: In this paper, we consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multiletter characterizations of two different two-dimensional capacity regions. The first region comprises the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.

Parameter Estimation of Quantum Channels

Abstract: The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit strictly; hence, no speedup is possible in its estimation. We also construct a class of nonunitary quantum channels whose parameter can be estimated in a way that the standard quantum limit is broken. The study of estimation of general quantum channels also enables an investigation of the effect of noises on quantum estimation.

Greenberger-Horne-Zeilinger versus W states: Quantum teleportation through noisy channels

Abstract: Which state loses less quantum information between Greenberger-Horne-Zeilinger (GHZ) and $W$ states when they are prepared for two-party quantum teleportation through a noisy channel? We address this issue by solving analytically a master equation in the Lindblad form with introducing the noisy channels that cause the quantum channels to be mixed states. It is found that the answer to this question is dependent on the type of noisy channel. If, for example, the noisy channel is $({L}_{2,x},{L}_{3,x},{L}_{4,x})$ type, where the $L$'s denote the Lindblad operators, the GHZ state is always more robust than the $W$ state, i.e., the GHZ state preserves more quantum information. In, however, the $({L}_{2,y},{L}_{3,y},{L}_{4,y})$-type channel the situation becomes completely reversed. In the $({L}_{2,z},{L}_{3,z},{L}_{4,z})$-type channel, the $W$ state is more robust than the GHZ state when the noisy parameter $(\ensuremath{\kappa})$ is comparatively small while the GHZ state becomes more robust when $\ensuremath{\kappa}$ is large. In isotropic noisy channel we found that both states preserve an equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.

Quantum key distribution without a shared reference frame

Abstract: We report a simple quantum-key-distribution experiment in which Alice and Bob do not need to share a common polarization direction in order to send information. Logical qubits are encoded into nonseparable states of polarization and first-order transverse spatial modes of the same photon.

Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations

Abstract: Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus.