dorsal/arxiv
View SchemaDiscrete time quantum walk model for single and entangled particles to retain entanglement in coin space
| Authors | C. M. Chandrashekar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609113 |
| URL | https://arxiv.org/abs/quant-ph/0609113 |
Abstract
In most widely discussed discrete time quantum walk model, after every unitary shift operator, the particle evolves into the superposition of position space and settles down in one of its basis states, loosing entanglement in the coin space in the new position. The Hadamard operation is applied to let the particle to evolve into the superposition in the coin space and the walk is iterated. We present a model with a additional degree of freedom for the unitary shift operator $U^{\prime}$. The unitary operator with additional degree of freedom will evolve the quantum particle into superposition of position space retaining the entanglement in coin space. This eliminates the need for quantum coin toss (Hadamard operation) after every unitary displacement operation as used in most widely studied version of the discrete time quantum walk model. This construction is easily extended to a multiple particle quantum walk and in this article we extend it for a pair of particles in pure state entangled in coin degree of freedom by simultaneously subjecting it to a pair of unitary displacement operators which were constructed for single particle. We point out that unlike for single particle quantum walk, upon measurement of its position after $N$ steps, the entangled particles are found together with 1/2 probability and at different positions with 1/2 probability. This can act as an advantage in applications of the quantum walk. A special case is also treated using a complex physical system such as, inter species two-particle entangled Bose-Einstein condensate, as an example.
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"abstract": "In most widely discussed discrete time quantum walk model, after every\nunitary shift operator, the particle evolves into the superposition of position\nspace and settles down in one of its basis states, loosing entanglement in the\ncoin space in the new position. The Hadamard operation is applied to let the\nparticle to evolve into the superposition in the coin space and the walk is\niterated. We present a model with a additional degree of freedom for the\nunitary shift operator $U^{\\prime}$. The unitary operator with additional\ndegree of freedom will evolve the quantum particle into superposition of\nposition space retaining the entanglement in coin space. This eliminates the\nneed for quantum coin toss (Hadamard operation) after every unitary\ndisplacement operation as used in most widely studied version of the discrete\ntime quantum walk model. This construction is easily extended to a multiple\nparticle quantum walk and in this article we extend it for a pair of particles\nin pure state entangled in coin degree of freedom by simultaneously subjecting\nit to a pair of unitary displacement operators which were constructed for\nsingle particle. We point out that unlike for single particle quantum walk,\nupon measurement of its position after $N$ steps, the entangled particles are\nfound together with 1/2 probability and at different positions with 1/2\nprobability. This can act as an advantage in applications of the quantum walk.\nA special case is also treated using a complex physical system such as, inter\nspecies two-particle entangled Bose-Einstein condensate, as an example.",
"arxiv_id": "quant-ph/0609113",
"authors": [
"C. M. Chandrashekar"
],
"categories": [
"quant-ph"
],
"title": "Discrete time quantum walk model for single and entangled particles to retain entanglement in coin space",
"url": "https://arxiv.org/abs/quant-ph/0609113"
},
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