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arXiv:1209.2958

Ququat as superposition of coherent state and their application in quantum information processing

Mishra, Manoj K, Hari Prakash, Vibhuti Bhushan Jha

Published Sep 13, 2012• 0 citations
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Abstract

Superposition of optical coherent states $\left|\pmα\right\rangle$, possessing opposite phases, play an important role as qubits in quantum information processing (QIP) tasks and are of fundamental importance in testing quantum mechanics. Passage of such superposition of coherent states (SCS) from a 50:50 beam splitter lead to generation of entangled coherent states. Recently, ququats and qutrits defined in four and three dimensional Hilbert space respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially require physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with $4n +j$ (here, $j =0, 1, 2$ or $3$, and $n = 0, 1, ..., \infty$) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher dimensional BB84 protocol in order to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different QIP tasks.

DOI
10.48550/arxiv.1209.2958

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Superposition of optical coherent states ∣±α⟩\left|\pmα\right\rangle∣±α⟩, possessing opposite phases, play an important role as qubits in quantum information processing (QIP) tasks and are of fundamental importance in testing quantum mechanics. Passage of such superposition of coherent states (SCS) from a 50:50 beam splitter lead to generation of entangled coherent states. Recently, ququats and qutrits defined in four and three dimensional Hilbert space respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially require physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with 4n+j4n +j4n+j (here, j=0,1,2j =0, 1, 2j=0,1,2 or 333, and n=0,1,...,∞n = 0, 1, ..., \inftyn=0,1,...,∞) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher dimensional BB84 protocol in order to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different QIP tasks.
Superposition of optical coherent states (SCS) [Formula: see text], possessing opposite phases, plays an important role as qubits in quantum information processing tasks like quantum computation, teleportation, key distribution, etc. and are of fundamental importance in testing quantum mechanics. Passage of such SCS from a 50:50 beam splitter leads to generation of entangled coherent states. Recently, ququats and qutrits defined in four- and three-dimensional Hilbert space, respectively, have attracted much attention as they offer advantage in secure quantum communication. However, practical utilization of these advantages essentially requires physical realization of quantum optical ququats and qutrits. Here, we define four new multi-photonic states (MPS) with [Formula: see text] (here, [Formula: see text] or 3 and [Formula: see text]) numbers of photon and show how the SCS can be used to encode ququat using these MPS as basis vectors of a four-dimensional Hilbert space. When these MPS fall upon a 50:50 beam splitter, the resulting states are bipartite four-component entangled coherent states (BFECS) equivalently representing the entangled ququats. We briefly discuss the photon statistical properties of such MPS and BFECS. We show that these MPS and BFECS can be synthesized using even coherent states as input to an interferometer. We give a simple linear optical protocol for almost perfect teleportation of a ququat encoded in SCS with the aid of BFECS as quantum channel. We also describe how these ququats can be used for realization of higher-dimensional BB84 protocol to increase the security of quantum key distribution. Finally, we discuss the possible advantages of using SCS as ququats and BFECS as quantum channel in different quantum information processing tasks.
Superposition of optical coherent states (SCS) Ket(plus/minus alpha), possessing opposite phases, plays an important role as qubits in quantum information processing tasks like quantum computation, teleportation, cryptography etc. and are of fundamental importance in testing quantum mechanics. Recently, ququats and qutrits defined in four and three dimensional (D) Hilbert space, respectively, have attracted much more attention as they present advantage in secure quantum communication and also in researches on the foundation of quantum mechanics. Here, we show that superposition of four non-orthogonal coherent states Ket(plus/minus alpha) and Ket(plus/minus i alpha), that are 90 degrees out of phase, can be employed for encoding one ququat defined in a 4D Hilbert space spanned by four newly defined multi-photonic states, Ket(alpha subscript j) with 4n+j numbers of photons, where, j= 0, 1, 2, 3. We propose a scheme which generates states Ket(alpha subscript j). When these states fall on a 50-50 beam splitter, the result is bipartite four-component entangled coherent state which represents equivalently an entangled ququat. Finally, we propose a linear optical scheme that gives almost perfect teleportation (minimum average fidelity greater than or equal to 0.99) of single ququat encoded in SCS using entangled ququat based on coherent states with almost perfect success rate for coherent amplitude mod(alpha) greater than or equal to 3.2. The present theoretical investigation and teleportation protocol is important in the sense that ququat allows the quantum information to be encoded and processed much more compactly and efficiently using fewer coupled quantum system.
The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing both the 3-4 dimensional case (both for maximally and non-maximally entanglement) and then the extension to an arbitrary dimension. Afterwards, we will discuss the theoretical results on using qudits for quantum communication, epitomizing the outcomes on a larger security in Quantum Key Distribution protocols (again considering separately qutrits, ququats and generalization to arbitrary dimension). Finally, we will present the experiments performed up to now for producing quantum optical qudits and their applications. In particular, we will mention schemes based on interferometric set-ups, orbital angular momentum entanglement and biphoton polarization. Finally, we will summarize what hyperentanglement is and its applications.
When a superposition $(|\ensuremath{\alpha}〉\ensuremath{-}|\ensuremath{-}\ensuremath{\alpha}〉)$ of two coherent states with opposite phase falls upon a 50-50 beam splitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of \ensuremath{\alpha}, as was recently discovered by Hirota and Sasaki [LANL e-print quant-ph/0101018]. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat states.
This paper outlines a linear-optical protocol for the teleportation of bipartite entangled coherent states (ECSs) using maximally ECSs as quantum channels. The scheme relies on symmetric beam splitters, phase shifters, photon-number-resolved measurements, and conditional local phase operations. Successful teleportation is achieved probabilistically with a constant success rate of 50%, independent of the coherent-state amplitude [Formula: see text], and governed by the parity of the measurement outcomes. The absence of nonlinear optical processes or direct photon interactions renders the protocol experimentally feasible and scalable, making it suitable for applications in continuous-variable quantum communication, quantum information processing, and coherent-state entanglement distribution.