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At least 343 records · Page 19Linked to original sources

arXiv2008

On quantum statistics in data analysis

Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the other hand, it is well known that the lattices of concepts, that arise in data analysis, are in general also non-distributive, albeit for completely different reasons. In his recent book, van Rijsbergen argues that many of the logical tools developed for quantum systems are also suitable for applications in information retrieval. I explore the mathematical support for this idea on an abstract vector space model, covering several forms of data analysis (information retrieval, data mining, collaborative filtering, formal concept analysis...), and roughly based on an idea from categorical quantum mechanics. It turns out that quantum (i.e., noncommutative) probability distributions arise already in this rudimentary mathematical framework. We show that a Bell-type inequality must be satisfied by the standard similarity measures, if they are used for preference predictions. The fact that already a very general, abstract version of the vector space model yields simple counterexamples for such inequalities seems to be an indicator of a genuine need for quantum statistics in data analysis.

cs.IR↗

arXiv2008

Single mode two-channel cavity QED

In this short communication, a new type of two-channel cavity QED model is derived. Two-channel models are important for they often lead to quantum interference phenomena. The previous models relied on the use of two or more modes of the quantized electromagnetic field, partially because of energy and parity restrictions. As it is shown in this work, such restrictions may be overcome with the use of properly chosen configurations of atomic levels and the aplication of classical external fields. Competing one- and two-photon processes involving one single mode may be obtained.

quant-ph↗

arXiv2008

Classification of the separable maps which preserve Werner states

We classify the completely-positive maps acting on two $d$-dimensional systems which commute with all $U\otimes U$ unitaries, where $U\in SU(d)$. This set of operations map Werner states to Werner states. We find a simple condition for a map being implementable by stochastic local operations and classical communication (SLOCC). We show that all PPT-preserving maps can be implemented by SLOCC. This can be used to prove that the entanglement of Werner states cannot be stochastically increased, even if we allow PPT entanglement for free.

quant-ph↗

arXiv2008

Quantum continual measurements: the spectrum of the output

When a quantum system is monitored in continuous time, the result of the measurement is a stochastic process. When the output process is stationary, at least in the long run, the spectrum of the process can be introduced and its properties studied. A typical continual measurement for quantum optical systems is the so called homodyne detection. In this paper we show how the Heisenberg uncertainty relations give rise to characteristic bounds on the possible homodyne spectra and we discuss how this is related to the typical quantum phenomenon of squeezing.

quant-ph↗

arXiv2008

Fidelity and Entanglement of a Spatially Extended Linear Three-Qubit Register

We study decoherence of a three-qubit array coupled to substrate phonons. Assuming an initial three-qubit entangled state that would be decoherence-free for identical qubit positions, allows us to focus on non-Markovian effects of the inevitable spatial qubit separation. It turns out that the coherence is most affected when the qubits are regularly spaced. Moreover, we find that up to a constant scaling factor, two-qubit entanglement is not influenced by the presence f the third qubit, even though all qubits interact via the phonon field.

cond-mat.mes-hall↗

arXiv2008

Concurrence of Stochastic 1-Qubit Maps

Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. By a new method we find the relevant convex roof pattern. We conclude that two component optimal decompositions always exist. Our results can be transferred to $2 \times n$-quantum systems providing the concurrence for all rank two density operators as well as a lower bound for their entanglement of formation.

quant-ph↗

arXiv2010

Mathematical framework for detection and quantification of nonclassical correlation

Existing measures of bipartite nonclassical correlation that is typically characterized by nonvanishing nonlocalizable information under the zero-way CLOCC protocol are expensive in computational cost. We define and evaluate economical measures on the basis of a new class of maps, eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps. The class is in analogy to the class of positive-but-not-completely-positive (PnCP) maps that have been commonly used in the entanglement theories. Linear and nonlinear EnCE maps are investigated. We also prove subadditivity of the measures in a form of logarithmic fidelity.

quant-ph↗

arXiv2008

The capacity of transmitting atomic qubit with light

The quantum information transfer between a single photon and a two-level atom is considered as a part of a quantum channel. The channel is a degradable channel even when there are decays of the atomic excited state and the single photon state, as far as the total excitation of the combined initial state does not exceed 1. The single letter formula for quantum capacity is obtained.

quant-ph↗

arXiv2008

Quantum computing, phase estimation and applications

In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA) is derived from the Kitaev phase estimation, a study of robustness of the IPEA utilized as a few-qubit testbed application is performed, and an improved protocol for phase reference alignment is presented. Additionally, a short overview of quantum cryptography is given, with a particular focus on quantum steganography and authentication.

quant-ph↗

arXiv2008

Security of entanglement-based quantum key distribution with practical detectors

We prove the unconditional security of an entanglement-based quantum-key-distribution protocol using detectors that respond to multiple modes of light and cannot distinguish between one from two or more photons. Even with such practical detectors, any defect in the source is automatically detected as an increase in the error rate or in the rate of double clicks.

quant-ph↗

arXiv2013

Optimal cooling of a driven artificial atom in dissipative environment

We study microwave-driven cooling in a superconducting flux qubit subjected to environment noises. For the weak decoherence, our analytical results agree well with the experimental observations near the degeneracy point and show that the microwave amplitude for optimal cooling should depend linearly on the dc flux detuning. With the decoherence increasing, more vibrational degrees of freedom couple in, making the ordinary cooling method less effective or even fail. We propose an improved cooling method, which can eliminate the perturbation of additional vibrational degrees of freedom hence keep high efficiency even under the strong decoherence. Furthermore, we point out that the decoherence will modulate the frequency where microwave-driven Landau-Zener transition reaches maximum in both methods, displaying the feature of incoherent dynamics which is important for the optimal cooling of qubits and other quantum systems.

quant-ph↗

arXiv2013

Electromagnetically induced interference at superconducting qubits

We study electromagnetically induced interference at superconducting qubits. The interaction between qubits and electromagnetic fields can provide additional coupling channels to qubit states, leading to quantum interference in a microwave driven qubit. In particular, the interwell relaxation or Rabi oscillation, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the qubits and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic frequency of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi oscillation, Rabi oscillation induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the qubit, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation, in not only the flux qubit but also the systems with no crossover structure, e.g. phase qubits.

quant-ph↗

arXiv2013

Decoherent histories of quantum searching

The theory of decoherent histories is an attempt to derive classical physics from positing only quantum laws at the fundamental level without notions of a classical apparatus or collapse of the wave-function. Searching for a marked target in a list of N items requires Ω(N) oracle queries when using a classical computer, while a quantum computer can accomplish the same task in O{\sqrt{N}} queries using Grover's quantum algorithm. We study a closed quantum system executing Grover algorithm in the framework of decoherent histories and find it to be an exactly solvable model, thus yielding an alternate derivation of Grover's famous result. We also subject the Grover-executing computer to a generic external influence without needing to know the specifics of the Hamiltonian insofar as the histories decohere. Depending on the amount of decoherence, which is captured in our model by a single parameter related to the amount of information obtained by the environment, the search time can range from quantum to classical. Thus, we identify a key effect induced by the environment that can adversely affect a quantum computer's performance and demonstrate exactly how classical computing can emerge from quantum laws.

quant-ph↗

arXiv2013

Global Completability with Applications to Self-Consistent Quantum Tomography

Let p_1, ..., p_N \in R^D be unknown vectors and let Omega \subseteq {1,...,N}^{\times 2}. Assume that the inner products p_i^T p_j are fixed for all (i,j) \in Omega. Do these inner product constraints (up to simultaneous rotation of all vectors) determine p_1, ..., p_N uniquely? Here we derive a necessary and sufficient condition for the uniqueness of p_1, ...,p_N (i.e., global completability) which is applicable to a large class of practically relevant sets Omega. Moreover, given Omega, we show that the condition for global completability is universal in the sense that for almost all vectors p_1, ...,p_N \in R^D the completability of p_1, ...,p_N only depends on Omega and not on the specific values of p_i^T p_j$ for (i,j) \in Omega. This work was motivated by practical considerations, namely, self-consistent quantum tomography.

quant-ph↗

arXiv2013

Efficient Inner-product Algorithm for Stabilizer States

Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that preserve them. Such states are obtained by stabilizer circuits (consisting of CNOT, Hadamard and Phase only) and can be represented compactly on conventional computers using Omega(n^2) bits, where n is the number of qubits. Although techniques for the efficient simulation of stabilizer circuits have been studied extensively, techniques for efficient manipulation of stabilizer states are not currently available. To this end, we design new algorithms for: (i) obtaining canonical generators for stabilizer states, (ii) obtaining canonical stabilizer circuits, and (iii) computing the inner product between stabilizer states. Our inner-product algorithm takes O(n^3) time in general, but observes quadratic behavior for many practical instances relevant to QECC (e.g., GHZ states). We prove that each n-qubit stabilizer state has exactly 4(2^n - 1) nearest-neighbor stabilizer states, and verify this claim experimentally using our algorithms. We design techniques for representing arbitrary quantum states using stabilizer frames and generalize our algorithms to compute the inner product between two such frames.

cs.ET↗

arXiv2013

Convolutional Codes Derived From Group Character Codes

New families of unit memory as well as multi-memory convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator matrices, consequently, they are non catastrophic. Additionally, the new code parameters are better than the ones available in the literature.

cs.IT↗

arXiv2013

Complementarity of quantum discord and classically accessible information

The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers -- information that is redundantly transmitted by the environment -- while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. Further, we prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective -- accessible to many observers -- only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.

quant-ph↗

arXiv2013

Multiparty quantum communication using multiqubit entanglement and teleportation

We propose a 2N qubit entangled channel that can be used to teleport N qubits in a network to a single receiver. We describe the construction of this channel and explicitly demonstrate how the protocol works. The protocol is different from teleportation using $N$ Bell pairs shared between $N$ senders and a single receiver, as it ensures that all parties have to participate in order for the teleportation to be successful. This can be advantageous in various scenarios and we discuss potential application of this protocol to voting.

quant-ph↗