# Questions tagged [quantum-operation]

For questions about completely positive (CP) linear maps between quantum states. Can also be used for trace-preserving CP maps (quantum channels). For questions about unitary operations, please use quantum-gate instead.

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### Confusing notation in Wikipedia's quantum channel article

In the Wikipedia's Quantum channel article, it is said that a purely quantum channel $\phi$ (it's not exactly the same phi calligraphy but it's close), in the Schrodinger picture, is a linear map ...
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### Is quantum deletion via a partial randomization procedure possible?

The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go ...
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### CPTP, Kraus representation and classical registers

What is the best mathematical representation of a quantum system that has some classical registers and some quantum registers? I'm asking because I'm considering any "physical" process $\pi()$ that ...
157 views

### Explicit form for composition of Choi representation quantum channels

Let $|\Omega \rangle$ be the maximally entangled state over a bipartite system whose parts are each dimension $d$, i.e. $$| \Omega \rangle \equiv \sum_i^{d}| ii \rangle$$ Then one way of writing ...
215 views

### How does qiskit finally implement a noise model?

I have been reading qiskit documentation for hours and I still don't get how does it implements noise in the circuit. I have understood that it works with a objects of the class QuantumError which ...
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### Proof that quantum entanglement does not increase the asymptotic capacity of classical channel

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the ...
76 views

### Simulating Classical Probabilistic Transitions with superoperators

I'm working on the following exercise: "Show how a classical probabilistic transition on an M -state system can be simulated by a quantum algorithm by adding an additional M -state ‘ancilla’ ...
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### How to obtain the tensor-product of two quantum operations (superoperators) explicitly?

I have an amplitude damping channel, denoted as a superoperator $\mathcal{E}$ with operator elements \begin{matrix} E_1=\begin{pmatrix} 1 & 0 \\ 0 & \sqrt{1-r} \end{pmatrix},\quad ...
515 views

### How is the partial trace related to the operator sum representation? [duplicate]

In Quantum Computation and Quantum Information by Nielsen and Chuang, the authors introduce operator sum representation in Section 8.2.3. They denote the evolution of a density matrix, when given an ...
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### What is the difference between intercept-resend attack and measure-resend attack?

I am going through different types of attacks that eve can perform on the quantum channel. I came across the intercept-resend attack and measure-resend attack. What is the difference between the two? ...
520 views

### How to define a quantum channel for the partial trace?

I understand that the partial trace is a linear map, a completely positive map and a trace-preserving map. However, I have no idea how to define a quantum channel with the partial trace because ...
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### What goes wrong if I try to simulate a system with a larger Hilbert space with a smaller Hilbert space?

System 1: This has a Hilbert space of dimension $N$. System 2: This has a Hilbert space of dimension $N'$, with the condition that $N' \ll N$. We want to simulate system 1 using the system 2, and so ...
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### If a state is only "close to" an eigenstate of an operator, how many applications of the operator does it take to scramble the state?

Suppose we have an operator $U$, and a register $|\lambda\rangle$ in an eigenstate of $U$ with eigenvalue $\lambda=1$. Repeatedly applying $U$ to $|\lambda\rangle$ does not affect $|\lambda\rangle$ - ...
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### The solution when we transmit a qubit through a Pauli channel?

A Pauli channel is defined as a convex combination of Pauli operators, i.e. $\epsilon_{\text{Pauli}} (\rho)=\sum_{j} q_j\sigma_j\rho \sigma_j$, where $0 \leq q_j \leq 1$ and $\sum_j q_j=1$. Now, I ...
233 views

### Is there a quantum operation whose output is always orthogonal to the input?

I'm trying to show/convince myself the following statement is correct (I haven't been able to find any similar posts): "There is no reversible quantum operation that transforms any input state to a ...
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### Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
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### Why does entanglement not increase the classical capacity of a channel?

In a recent paper, the authors quote an older work of Bennett, Shor and others and make the following statement While entanglement assistance can increase achievable rates for classical point-to-...
131 views

### Why can any LOCC operation be written as $\sum_k (A_k\otimes B_k)\rho(A_k^\dagger\otimes B_k^\dagger)$?

This statement can be found in Vedral et al. 1997, eq. (1). More precisely, given a bipartite state $\rho_{AB}$, they claim that any operation on $\rho_{AB}$ involving local operations plus classical ...
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### Counting channel uses of the lossy bosonic channel or definition of channel uses

The PLOB-bound ("Fundamental Limits of Repeaterless Quantum Communications") gives an asymptotic upper bound on the secret-key rate per used lossy bosonic channel. However, I'm not sure how to count ...
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### What is the relevance of preservation of trace in completely postive trace preserving (CPTP) maps?

Why is the trace preserving part necessary? Is it not enough if it can take all matrices to matrices of trace 1?
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### Implementing a depolarizing channel for 2 qubits on IBM Q

I am trying to use IBM Q to perform the following depolarizing channel on a state of 2 qubits $\rho=|\psi \rangle \langle \psi |$: $$\rho \to (1-\lambda)\rho + \frac{\lambda}{4}I$$ This is within ...
232 views

### How should we interpret these quantum logic gates as physical observables?

In quantum mechanics each operator corresponds to some physical observable, but say we have the operators $X,Y,Z,H, \operatorname{CNOT}$. I understand how these gates act on qubits, but what do they ...
It is said in a lecture note by John Preskill that, Equivalently, we may imagine measuring system $B$ in the basis $\{|a\rangle\}$, but failing to record the measurement outcome, so we are ...
Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)? Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM ...