/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q1E |蠄鈥郝=12|00鈥+12|11鈥篿s one... [FREE SOLUTION] | 91影视

91影视

|=12|00+12|11is one of the famous 鈥淏ell states,鈥 a highly entangled state of its two qubits. In this question we examine some of its strange properties. (a) Suppose this Bell state could be decomposed as the (tensor) product of two qubits (recall the box on page ), the first in state 0|0+1|1and the second in state0|0+1|1. Write four equations that the amplitudes 0,1,0and1must satisfy. Conclude that the Bell state cannot be so decomposed.

(b) What is the result of measuring the first qubit of |?

(c) What is the result of measuring the second qubit after measuring the first qubit? (d) If the two qubits in state| are very far from each other, can you see why the answer to (c) is surprising?

Short Answer

Expert verified

a. The required four equations are:

  • |=0|0+0|1
  • |0|2+|0|2=1
  • |x1=0|0+1|1
  • |x2=0|0+2|1

Where,x1and|x2andare two quantum states.

b. The measure of first qubit state |is|0is with probability ..

c. The measure of first qubit state |is|0is with probability..

d. No matter how far the two qubits are, yet their value will be same.

Step by step solution

01

Solution (a)

Now there are following four equations that satisfied the amplitudes:

  • |=0|0+0|1
  • |=0|0+0|1
  • |x1=0|0+1|1
  • |x2=0|0+2|1

Here, |x1and|x2are two quantum states.

Let, |=1200+1211

Similarly, |=x0.y0|00+x0.y1|01+x1

Hence,

x0.y0=12x0.y1=x1.y0=0

Therefore,x1.y1=12andx1.y0=0

But then, localid="1658915843438" x0.y0=0orx1.y1=0. This is not according to the consumption made.

Hence, we cannot be decompose in the above manner.

02

Solution (b)

The qubit can be calculated in two ways with the value 0and1which will be most common outcome. But a qubit state can be superimposed of 0and1

Like, the measure of first qubit state |is|0which have occurrence probability of and for second qubit state 1is also 12.

By using this way, we can measure the first qubit of |

03

Solution (c)

The second qubit can be measure in same way as that of first qubit in solution(b). And the value of second qubit will be same as that of first qubit, where, the second qubit state of |is|1is also.

04

Solution (d)

No matter how far the two qubits are, yet their value will be same.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A vertex cover of a graph G=(V,E)is a subset of vertices SVthat includes at least one endpoint of every edge in E. Give a linear-time algorithm for the following task.

Input: An undirected tree T=(V,E).

Output: The size of the smallest vertex cover of T. For instance, in the following tree, possible vertex covers include{A,B,C,D,E,F,G}and{A,C,D,F}but not{C,E,F}.The smallest vertex cover has size 3: {B,E,G}.

Alice wants to throw a party and is deciding whom to call. She has n people to choose from, and she has made up a list of which pairs of these people know each other. She wants to pick as many people as possible, subject to two constraints: at the party, each person should have at least five other people whom they know and five other people whom they don鈥檛 know. Give an efficient algorithm that takes as input the list of n people and the list of pairs who know each other and outputs the best choice of party invitees. Give the running time in terms of n

Consider the following game. A 鈥渄ealer鈥 produces a sequence s1sn of 鈥渃ards,鈥 face up, where each card si has a value vi. Then two players take turns picking a card from the sequence, but can only pick the first or the last card of the (remaining) sequence. The goal is to collect cards of largest total value. (For example, you can think of the cards as bills of different denominations.) Assume n is even. (a) Show a sequence of cards such that it is not optimal for the first player to start by picking up the available card of larger value. That is, the natural greedy strategy is suboptimal. (b) Give an O(n2) algorithm to compute an optimal strategy for the first player. Given the initial sequence, your algorithm should precompute in O(n2) time some information, and then the first player should be able to make each move optimally in O(1) time by looking up the precomputed information.

Here鈥檚 a problem that occurs in automatic program analysis. For a set of variablesx1,......,xn, you are given some equality constraints, of the form 鈥 xi=xj鈥 and some disequality constraints, of the form 鈥 xixj.鈥 Is it possible to satisfy all of them?

For instance, the constraints.

x1=x2,x2=x3,x3=x4,x1x4

cannot be satisfied. Give an efficient algorithm that takes as input m constraints over n variables and decides whether the constraints can be satisfied.

The kSPANNING TREE problem is the following.Input: An undirected graph G=(V,E) Output: A spanning tree of G in which each node has degree k, if such a tree exists.Show that for any k2:

  1. k SPANNING TREE is a search problem.
  2. k SPANNING TREE is NP-complete. (Hint: Start with k=2 and consider the relation between this problem and RUDRATA PATH.)
See all solutions

Recommended explanations on Computer Science Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.