Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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5 votes
3 answers
197 views

$M(\rho)=\operatorname{Tr}_2[U(\rho\otimes\rho_2)U^{\dagger}]$ is unitary $\iff U=U_1\otimes U_2$, a product of $2$ unitary operators?

Let $\rho : V_1 \to V_1 $ and $\rho_2 : V_2 \to V_2 $, where $V_1$ and $V_2$ are Hilbert spaces. Suppose that $U:V_1\otimes V_2 \to V_1\otimes V_2$ is a unitary operator. Define a map $M : L(V_1, ...
0 votes
0 answers
40 views

How cat state is constructed?

Context: On Wikipedia, a cat state (2-component) is defined as $$ |\text{cat}_+\rangle = C_+(|\alpha\rangle + |-\alpha\rangle) $$ $$ |\text{cat}_-\rangle = C_-(|\alpha\rangle - |-\alpha\rangle), $$ ...
4 votes
2 answers
214 views

Can a non-local unitary operator preserve separability

Consider a $2$-qubit system with Hilbert space $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$. A pure separable state in $\mathcal{H}$ is of the form $\lvert \psi_1 \rangle \otimes \lvert \...
1 vote
1 answer
104 views

How many single and double qubit gates are required to create a uniform superposition of vertices of a Johnson Graph J(n,r)?

Can I in $\tilde{O}(r)$ number of gates (single and double qubit) create a uniform superposition of vertices of Johnson Graph $J(n,r)$? I would like to create a state $|\psi\rangle = \frac{1}{\sqrt{n \...
3 votes
0 answers
66 views
+50

Almost perfect quantum encryption of a mixed state using only $n + O(\log(n) +\log(\frac{1}{\epsilon}))$ shared bits

Alice holds a state $\psi$ of $n$-qubits, and wants to send it to Bob using a single quantum message. Bob and Alice share only $n + O(log(n) +log(\frac{1}{\epsilon}))$ random bits, for some value $\...
8 votes
1 answer
524 views

Is there a comprehensive list of counterexamples in quantum information?

As was already asked about in this phys.SE question many years ago---which, sadly, got closed and never received an answer---is there a collection of counterexamples in quantum information theory, &...
1 vote
0 answers
49 views

State tomography in Qiskit on a subset of qubits of real QPU

Could anyone please explain how should I carry out a state tomography on a real device in Qiskit (version 0.43.2)? I have access to devices with 127 qubits, but I want to perform a simulation using ...
1 vote
1 answer
59 views

Proability of measuing a qubit in a two qubit system without having a perpendicular basis

I am trying to understand how to apply Born's rule on two qubit systems. From class, the teacher told us that we can write the state like so: only if $\theta_0$ and $\theta_1$ are ortogonal. But now ...
3 votes
2 answers
247 views

Prove that there is no polynomial size quantum algorithm for a Simon's problem with no promise on the input

We look at the following variant of Simon's problem. There is an algorithm $A$ that solves a problem with the following settings: The input is an oracle $f:\{0,1\}^n \to [M]$. The output of the ...
2 votes
1 answer
57 views

To understand the notation of $| a, a \oplus b \rangle$

This must be trivial but I can't find a clear explanation of the notation of $| a, a \oplus b \rangle$. It is the resulting state after applying a CNOT gate to $|a,b\rangle$: $\rm{CNOT}|a,b\rangle = | ...
4 votes
3 answers
581 views

Creating a uniform superposition of a subset of basis states

Assume we have an n qubit system and $K \subset \{1,...,2^n\}, K \neq \emptyset $ I want to describe a circuit that takes the input $|0\rangle....|0\rangle$ to the state $|\psi\rangle = \frac{1}{\sqrt{...
3 votes
2 answers
91 views

Are measurements in $X$ and $Z$ bases being equal enough to prove equality of quantum states?

Suppose I have two single qubit states $\rho$ and $\sigma$. In my example, they are pure but I keep it general here. Suppose I know that $$\text{Tr}(\vert +\rangle\langle +\vert\rho) = \text{Tr}(\vert ...
6 votes
2 answers
553 views

Prove the fidelity can be written in terms of Pauli expectation values as ${\rm tr}(\rho\sigma)=\sum_k \chi_\rho(k)\chi_\sigma(\rho)$

I am reading through "Direct Fidelity Estimation from Few Pauli Measurements" and it states that the measure of fidelity between a desired pure state $\rho$ and an arbitrary state $\sigma$ ...
5 votes
2 answers
1k views

What is the IQ plane?

I struggle to find any information on Nielsen and Chuang or similar texts on the exact definition of the so-called IQ plane (I think this is a notion closely related to solid state quantum computers ...
4 votes
1 answer
498 views

Show that quantum channels act as affine transformations in the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture ...
0 votes
0 answers
22 views

What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
7 votes
2 answers
300 views

How can quantum error correction correct small rotations/continuous errors?

I'm having trouble understanding the so-called "digitization of errors" argument in QEC. Suppose I have to encode my logical qubit into $n$ physical qubits to do error correction. I will use ...
4 votes
2 answers
94 views

Show that all extensions of $\rho$ can be obtained as a channel applied to its purification

I am struggling with this exercise here: Let $H:A, H_E$ and $H_{E′}$ denote complex Euclidean spaces. Consider a purification $|ψ_{AE}⟩⟨ψ_{AE}| ∈ D(H_A ⊗ H_E)$ of a quantum state $ρ_A ∈ D(H_A)$ and a ...
0 votes
1 answer
55 views

How to convert one state of a quantum system to a desired state?

I have a state of 3 qubits: The first number inside the brackets gives the probability of each state, and the second number gives the phase. $$\begin{align} |000\rangle &= (12.5,0^{°}),\\ |001\...
1 vote
2 answers
56 views

How to generate the Bell state $\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$ from the state $|00\rangle$ using Qiskit?

I want to generate the Bell state $(|01\rangle+|10\rangle)/\sqrt{2}$ from the state $|00\rangle$ in qiskit, applying the Hadamard gate followed by the $\text{CNOT}$ gate. But it generates $(|11\rangle-...
1 vote
1 answer
193 views

How is phase kickback possible if qubits are unentangled?

If I have two independent (unentangled) qubits, let's say one in state |1> and the other one in some superposition state with equal amplitudes and arbitrary phases. If I measure the qubit that is ...
2 votes
1 answer
102 views

How to get $\theta$ and $\phi$ in a Bloch sphere for individual qubits in a quantum register?

I have a quantum register with some qubits (I'm just new to all of this). Is there a way to achieve $\theta$ and $\phi$ angle values in the Bloch sphere for each qubit separately? If I do a circuit ...
3 votes
1 answer
152 views

Why is the coefficient-squared the probability, and not just the coefficient itself?

Context: I have decided not to accept the postulates of quantum mechanics blindly as gospel. There must be a way someone arrived at those postulates, and I want to know the basic reasoning behind them,...
2 votes
2 answers
57 views

How to create a qudit of any dimension $d$ in qiskit?

How to create qudit, not qubit (which is a special case of qudit with $d = 2$) in qiskit of any dimension $d$? Actually, I searched this on chatgpt, but not-so-helpful info was found. It just uses ...
0 votes
2 answers
48 views

How can I get the state of my quantum circuit like save_statevector() in qiskit 1.0.2?

Just as the title, I want to get the state of my quantum circuit when running simulation locally with fake provider. But I cannot use save_statevector since Aer has been removed from qiskit. My code ...
2 votes
1 answer
64 views

Getting rid of extra qubits without changing phase

If I have the state $\frac{1}{\sqrt2}|0000\rangle + \frac{e^{i\phi}}{\sqrt2}|1111\rangle$ and need to get $\frac{1}{\sqrt2}|0\rangle + \frac{e^{i\phi}}{\sqrt2}|1\rangle$, does anyone have any ideas ...
2 votes
2 answers
57 views

Can Interaction with the environment cause $|0\rangle$ to evolve into a superposition like $|+\rangle$?

We say if a qubit is in state $|0\rangle$, and it is possible if it interacts with the environment it can result in a bit flip to a state $|1\rangle$, so I was wondering why can't it go to a ...
0 votes
1 answer
181 views

qiskit: convert from ising result to qubo result?

I have a very simple qubo problem: ...
1 vote
3 answers
176 views

Equivalence of quantum circuits

I have these 2 quantum circuits: Are they equivalent?I think they are but I cannot understand how this could be possible.Lets assume that the initial condition of the first circuit is:] Lets assume ...
2 votes
1 answer
47 views

Existence of a two-outcome measurement $M$ such that the induced distributions differs between different density matrices

Let $\rho \neq \sigma$ be density matrices. I want to show that there exists a two-outcome measurement $M$ such that the induced distributions $M(\rho)$ and $M(\sigma)$ differ. From what I learned, ...
1 vote
1 answer
53 views

How many times the circuit need to run when i use get_stateVector in qiskit

In qiskit,i use get_statevector method to get the statevector from my circuit. What i want to know is how many times the circuit need to run. Does is it only one? ...
2 votes
0 answers
19 views

Interested in software helping with projecting multi-qubit states onto irreducible components

My interest in QC comes from a problem in geometry called the Atiyah problem on configurations of points. In short, there is a nice one-to-one correspondence between quantum states of a single qubit ...
2 votes
3 answers
131 views

Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state?

Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state? Or does a quantum state need to be a superposition of the entire basis, i.e., $$ |A\rangle = \frac{1}{...
2 votes
1 answer
51 views

What is the difference between symmetric states and geometrically uniform states?

On the one hand, in this article, symmetric states are defined as: The $M$ symmetric quantum states which should be distinguished by means of the quantum measurement are described by statistical ...
0 votes
1 answer
37 views

Efficient computation of probabilities for an N-particle state

Suppose we have a state that is written as: \begin{eqnarray} |\Psi\rangle=\frac{1}{\mathcal{N}}\sum_{\mathcal{P}}e^{i\phi_p}\phi_{1p}(x_{1p})\phi_{2p}(x_{2p})...\phi_{N_p}(x_{N_p})|x_{1p}...x_{Np}\...
1 vote
0 answers
46 views

State amplification in Grover when starting with W state

I have two 3-qubit registers, each one is prepared in $W$ state, so my two registers are in state: $$\left|W_3\right\rangle\otimes \left|W_3\right\rangle \ ,$$I use this (6-qubits) diffusion operator ...
1 vote
0 answers
32 views

How to obtain this measurment result for arbitrary qubits in $X$ basis?

I have seen the following claim. Suppose one has two qubits $\vert\psi\rangle = a\vert 0\rangle + b\vert 1\rangle$ and $\vert\phi\rangle =a'\vert 0\rangle + b'\vert 1\rangle$ and both are measured in ...
3 votes
2 answers
239 views

Is it always possible to write the state corresponding to a set of stabilizer generators?

Given a set of stabilizer generators, is it always possible to write down the state corresponding to it? Is there a way to write down the quantum state corresponding to a stabilizer generator?
3 votes
1 answer
151 views

Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings. Say you ...
15 votes
3 answers
884 views

How to compactly represent multiple qubit states?

Since access to quantum devices capable of quantum computing is still extremely limited, it is of interest to simulate quantum computations on a classical computer. Representing the state of $n$ ...
2 votes
1 answer
274 views

Deriving the choi matrix definition of the quantum depolarizing channel

I was reading up on the quantum depolarizing channel (Preskill's Notes) (stack exchaange explanation), and I'm failing to see how the form \begin{align} \sigma &= (\mathcal E \otimes \mathbb I)(|\...
0 votes
1 answer
51 views

How can I shift elements around in my state vector according to a specific pattern?

Consider the statevector $|\psi_1\rangle=(a_0,...,a_{N-1})^T$. My goal is to shift the elements around to end up with $|\psi_2\rangle=(a_{3N/4},...,a_{N-1},a_0,...a_{N/2},\vec{\phi})^T$ where $\vec{\...
1 vote
1 answer
79 views

On difference in the number of two-qubit stabilizer states that are separable (36) vs those that are maximally entangled (24) and partial entanglement

We have a set of two-qubit stabilizer states. There are 60 of them: 36 separable and 24 maximally entangled (MES). I was wondering whether we can somehow compare the size of the set of partially ...
28 votes
3 answers
9k views

What are magic states?

I wonder what are magic states, and a magic state gadget. While I'm reading a paper, these terms frequently appear.
8 votes
3 answers
261 views

Is there a convention for denoting $Y$ eigenstates?

Two common shorthands for eigenstates of the $Z$ operator are $\{|0\rangle,|1\rangle\}$ and $\{|1\rangle,|-1\rangle\}$, where in the first case we have $Z|z\rangle=(-1)^z|z\rangle$ and in the second ...
43 votes
1 answer
2k views

Quantum machine learning after Ewin Tang

Recently, a series of research papers have been released (this, this and this, also this) that provide classical algorithms with the same runtime as quantum machine learning algorithms for the same ...
1 vote
2 answers
110 views

How to use get_statevector in Qiskit SDK 1.0?

I am Using Qiskit SDK 1.0. I have a problem with get_statevector in qiskit SDK 1.0 and using BasicSimulator. My code is attached ...
1 vote
1 answer
41 views

Projective measurement notation

I don't understand how projective measurements work; I think my confusion comes from the notation. How would this be written in matrix notation? Is it just [w row vector] [Ma matrix] [w column vector]^...
1 vote
1 answer
54 views

References for mapping qudit gates to qubits equivalent

Let's assume that I'm modelling a d-levels qudit as a set of n qubits, where $d = 2^n$. I would need to map the application of quantum gates on the qudit to a set of operations of the relative qubits ...
1 vote
1 answer
57 views

Is there a proof that any pure two-qubit Partially entangled state lies somewhere in between a separable and maximally entangled state?

Intuitively this seems true, but is there a proof of the following: We have two-qubit pure state. Given a Partially entangled state (PES) $|P\rangle$ we can always find a separable state $|S\rangle$, ...

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