Program.cs

static void Main(string[] args)
{
    int threadId = Task.Run(() =>
    {
        CallContext.LogicalSetData("k", 0);
        Console.WriteLine("Write logical data on thread " + Thread.CurrentThread.ManagedThreadId);
        return Thread.CurrentThread.ManagedThreadId;
    }).Result;

    while (true)
    {
        var tcs = new TaskCompletionSource<Tuple<int, object>>();
        Task.Run(() =>
        {
            tcs.SetResult(Tuple.Create(Thread.CurrentThread.ManagedThreadId, CallContext.LogicalGetData("k")));
            if (Thread.CurrentThread.ManagedThreadId != threadId)
                Thread.Sleep(3000);
        });
        var result = tcs.Task.Result;
        if (result.Item1 == threadId)
        {
            Console.WriteLine("Read logical data from thread " + result.Item1 + ": " + result.Item2);
            break;
        }
    }

    Console.ReadKey();
}